diff --git a/README.md b/README.md
index 41935f1..4c2a0af 100644
--- a/README.md
+++ b/README.md
@@ -36,6 +36,7 @@
 - Vanilla Imitation Learning
 - [Discrete Batch-Constrained deep Q-Learning (BCQ-Discrete)](https://arxiv.org/pdf/1910.01708.pdf)
 - [Discrete Conservative Q-Learning (CQL-Discrete)](https://arxiv.org/pdf/2006.04779.pdf)
+- [Discrete Critic Regularized Regression (CRR-Discrete)](https://arxiv.org/pdf/2006.15134.pdf)
 - [Prioritized Experience Replay (PER)](https://arxiv.org/pdf/1511.05952.pdf)
 - [Generalized Advantage Estimator (GAE)](https://arxiv.org/pdf/1506.02438.pdf)
 - [Posterior Sampling Reinforcement Learning (PSRL)](https://www.ece.uvic.ca/~bctill/papers/learning/Strens_2000.pdf)
diff --git a/docs/api/tianshou.policy.rst b/docs/api/tianshou.policy.rst
index aa17040..32f124f 100644
--- a/docs/api/tianshou.policy.rst
+++ b/docs/api/tianshou.policy.rst
@@ -104,6 +104,11 @@ Imitation
    :undoc-members:
    :show-inheritance:
 
+.. autoclass:: tianshou.policy.DiscreteCRRPolicy
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
 Model-based
 -----------
 
diff --git a/docs/index.rst b/docs/index.rst
index 72f479d..c0a3c02 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -26,6 +26,7 @@ Welcome to Tianshou!
 * :class:`~tianshou.policy.ImitationPolicy` Imitation Learning
 * :class:`~tianshou.policy.DiscreteBCQPolicy` `Discrete Batch-Constrained deep Q-Learning <https://arxiv.org/pdf/1910.01708.pdf>`_
 * :class:`~tianshou.policy.DiscreteCQLPolicy` `Discrete Conservative Q-Learning <https://arxiv.org/pdf/2006.04779.pdf>`_
+* :class:`~tianshou.policy.DiscreteCRRPolicy` `Critic Regularized Regression <https://arxiv.org/pdf/2006.15134.pdf>`_
 * :class:`~tianshou.policy.PSRLPolicy` `Posterior Sampling Reinforcement Learning <https://www.ece.uvic.ca/~bctill/papers/learning/Strens_2000.pdf>`_
 * :class:`~tianshou.data.PrioritizedReplayBuffer` `Prioritized Experience Replay <https://arxiv.org/pdf/1511.05952.pdf>`_
 * :meth:`~tianshou.policy.BasePolicy.compute_episodic_return` `Generalized Advantage Estimator <https://arxiv.org/pdf/1506.02438.pdf>`_
diff --git a/examples/atari/README.md b/examples/atari/README.md
index eb49a02..fb45858 100644
--- a/examples/atari/README.md
+++ b/examples/atari/README.md
@@ -99,3 +99,20 @@ Buffer size 10000:
 | ---------------------- | ---------- | ---------- | --------------------------------- | ------------------------------------------------------------ |
 | PongNoFrameskip-v4     | 20.5         | nan        | 1.8 (epoch 5)                      | `python3 atari_cql.py --task "PongNoFrameskip-v4" --load-buffer-name log/PongNoFrameskip-v4/qrdqn/expert.size_1e4.hdf5 --epoch 5 --min-q-weight 1` |
 | BreakoutNoFrameskip-v4 | 394.3        | 31.7       | 22.5 (epoch 12) | `python3 atari_cql.py --task "BreakoutNoFrameskip-v4" --load-buffer-name log/BreakoutNoFrameskip-v4/qrdqn/expert.size_1e4.hdf5 --epoch 12 --min-q-weight 10` |
+
+# CRR
+
+To running CRR algorithm on Atari, you need to do the following things:
+
+- Train an expert, by using the command listed in the above QRDQN section;
+- Generate buffer with noise: `python3 atari_qrdqn.py --task {your_task} --watch --resume-path log/{your_task}/qrdqn/policy.pth --eps-test 0.2 --buffer-size 1000000 --save-buffer-name expert.hdf5` (note that 1M Atari buffer cannot be saved as `.pkl` format because it is too large and will cause error);
+- Train CQL: `python3 atari_crr.py --task {your_task} --load-buffer-name expert.hdf5`.
+
+We test our CRR implementation on two example tasks (different from author's version, we use v4 instead of v0; one epoch means 10k gradient step):
+
+| Task                   | Online QRDQN | Behavioral | CRR            | CRR w/ CQL        | parameters                                                   |
+| ---------------------- | ---------- | ---------- | ---------------- | ----------------- | ------------------------------------------------------------ |
+| PongNoFrameskip-v4     | 20.5         | 6.8        | -21 (epoch 5)   |  16.1 (epoch 5)  | `python3 atari_crr.py --task "PongNoFrameskip-v4" --load-buffer-name log/PongNoFrameskip-v4/qrdqn/expert.hdf5 --epoch 5` |
+| BreakoutNoFrameskip-v4 | 394.3        | 46.9       | 26.4 (epoch 12) | 125.0 (epoch 12) | `python3 atari_crr.py --task "BreakoutNoFrameskip-v4" --load-buffer-name log/BreakoutNoFrameskip-v4/qrdqn/expert.hdf5 --epoch 12 --min-q-weight 50` |
+
+Note that CRR itself does not work well in Atari tasks but adding CQL loss/regularizer helps.
diff --git a/examples/atari/atari_crr.py b/examples/atari/atari_crr.py
new file mode 100644
index 0000000..6bd9167
--- /dev/null
+++ b/examples/atari/atari_crr.py
@@ -0,0 +1,155 @@
+import os
+import torch
+import pickle
+import pprint
+import datetime
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.utils import BasicLogger
+from tianshou.env import SubprocVectorEnv
+from tianshou.trainer import offline_trainer
+from tianshou.utils.net.discrete import Actor
+from tianshou.policy import DiscreteCRRPolicy
+from tianshou.data import Collector, VectorReplayBuffer
+
+from atari_network import DQN
+from atari_wrapper import wrap_deepmind
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--task", type=str, default="PongNoFrameskip-v4")
+    parser.add_argument("--seed", type=int, default=1626)
+    parser.add_argument("--lr", type=float, default=0.0001)
+    parser.add_argument("--gamma", type=float, default=0.99)
+    parser.add_argument("--policy-improvement-mode", type=str, default="exp")
+    parser.add_argument("--ratio-upper-bound", type=float, default=20.)
+    parser.add_argument("--beta", type=float, default=1.)
+    parser.add_argument("--min-q-weight", type=float, default=10.)
+    parser.add_argument("--target-update-freq", type=int, default=500)
+    parser.add_argument("--epoch", type=int, default=100)
+    parser.add_argument("--update-per-epoch", type=int, default=10000)
+    parser.add_argument("--batch-size", type=int, default=32)
+    parser.add_argument('--hidden-sizes', type=int, nargs='*', default=[512])
+    parser.add_argument("--test-num", type=int, default=10)
+    parser.add_argument('--frames-stack', type=int, default=4)
+    parser.add_argument("--logdir", type=str, default="log")
+    parser.add_argument("--render", type=float, default=0.)
+    parser.add_argument("--resume-path", type=str, default=None)
+    parser.add_argument("--watch", default=False, action="store_true",
+                        help="watch the play of pre-trained policy only")
+    parser.add_argument("--log-interval", type=int, default=100)
+    parser.add_argument(
+        "--load-buffer-name", type=str,
+        default="./expert_DQN_PongNoFrameskip-v4.hdf5")
+    parser.add_argument(
+        "--device", type=str,
+        default="cuda" if torch.cuda.is_available() else "cpu")
+    args = parser.parse_known_args()[0]
+    return args
+
+
+def make_atari_env(args):
+    return wrap_deepmind(args.task, frame_stack=args.frames_stack)
+
+
+def make_atari_env_watch(args):
+    return wrap_deepmind(args.task, frame_stack=args.frames_stack,
+                         episode_life=False, clip_rewards=False)
+
+
+def test_discrete_crr(args=get_args()):
+    # envs
+    env = make_atari_env(args)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    # should be N_FRAMES x H x W
+    print("Observations shape:", args.state_shape)
+    print("Actions shape:", args.action_shape)
+    # make environments
+    test_envs = SubprocVectorEnv([lambda: make_atari_env_watch(args)
+                                  for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    test_envs.seed(args.seed)
+    # model
+    feature_net = DQN(*args.state_shape, args.action_shape,
+                      device=args.device, features_only=True).to(args.device)
+    actor = Actor(feature_net, args.action_shape, device=args.device,
+                  hidden_sizes=args.hidden_sizes, softmax_output=False).to(args.device)
+    critic = DQN(*args.state_shape, args.action_shape,
+                 device=args.device).to(args.device)
+    optim = torch.optim.Adam(list(actor.parameters()) + list(critic.parameters()),
+                             lr=args.lr)
+    # define policy
+    policy = DiscreteCRRPolicy(
+        actor, critic, optim, args.gamma,
+        policy_improvement_mode=args.policy_improvement_mode,
+        ratio_upper_bound=args.ratio_upper_bound, beta=args.beta,
+        min_q_weight=args.min_q_weight,
+        target_update_freq=args.target_update_freq
+    ).to(args.device)
+    # load a previous policy
+    if args.resume_path:
+        policy.load_state_dict(torch.load(
+            args.resume_path, map_location=args.device))
+        print("Loaded agent from: ", args.resume_path)
+    # buffer
+    assert os.path.exists(args.load_buffer_name), \
+        "Please run atari_qrdqn.py first to get expert's data buffer."
+    if args.load_buffer_name.endswith('.pkl'):
+        buffer = pickle.load(open(args.load_buffer_name, "rb"))
+    elif args.load_buffer_name.endswith('.hdf5'):
+        buffer = VectorReplayBuffer.load_hdf5(args.load_buffer_name)
+    else:
+        print(f"Unknown buffer format: {args.load_buffer_name}")
+        exit(0)
+
+    # collector
+    test_collector = Collector(policy, test_envs, exploration_noise=True)
+
+    # log
+    log_path = os.path.join(
+        args.logdir, args.task, 'crr',
+        f'seed_{args.seed}_{datetime.datetime.now().strftime("%m%d-%H%M%S")}')
+    writer = SummaryWriter(log_path)
+    writer.add_text("args", str(args))
+    logger = BasicLogger(writer, update_interval=args.log_interval)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        return False
+
+    # watch agent's performance
+    def watch():
+        print("Setup test envs ...")
+        policy.eval()
+        test_envs.seed(args.seed)
+        print("Testing agent ...")
+        test_collector.reset()
+        result = test_collector.collect(n_episode=args.test_num,
+                                        render=args.render)
+        pprint.pprint(result)
+        rew = result["rews"].mean()
+        print(f'Mean reward (over {result["n/ep"]} episodes): {rew}')
+
+    if args.watch:
+        watch()
+        exit(0)
+
+    result = offline_trainer(
+        policy, buffer, test_collector, args.epoch,
+        args.update_per_epoch, args.test_num, args.batch_size,
+        stop_fn=stop_fn, save_fn=save_fn, logger=logger)
+
+    pprint.pprint(result)
+    watch()
+
+
+if __name__ == "__main__":
+    test_discrete_crr(get_args())
diff --git a/test/discrete/test_il_crr.py b/test/discrete/test_il_crr.py
new file mode 100644
index 0000000..736edef
--- /dev/null
+++ b/test/discrete/test_il_crr.py
@@ -0,0 +1,110 @@
+import os
+import gym
+import torch
+import pickle
+import pprint
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.data import Collector
+from tianshou.utils import BasicLogger
+from tianshou.env import DummyVectorEnv
+from tianshou.utils.net.common import Net
+from tianshou.trainer import offline_trainer
+from tianshou.policy import DiscreteCRRPolicy
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--task", type=str, default="CartPole-v0")
+    parser.add_argument("--seed", type=int, default=1626)
+    parser.add_argument("--lr", type=float, default=7e-4)
+    parser.add_argument("--gamma", type=float, default=0.99)
+    parser.add_argument("--n-step", type=int, default=3)
+    parser.add_argument("--target-update-freq", type=int, default=320)
+    parser.add_argument("--epoch", type=int, default=5)
+    parser.add_argument("--update-per-epoch", type=int, default=1000)
+    parser.add_argument("--batch-size", type=int, default=64)
+    parser.add_argument('--hidden-sizes', type=int,
+                        nargs='*', default=[64, 64])
+    parser.add_argument("--test-num", type=int, default=100)
+    parser.add_argument("--logdir", type=str, default="log")
+    parser.add_argument("--render", type=float, default=0.)
+    parser.add_argument(
+        "--load-buffer-name", type=str,
+        default="./expert_DQN_CartPole-v0.pkl",
+    )
+    parser.add_argument(
+        "--device", type=str,
+        default="cuda" if torch.cuda.is_available() else "cpu",
+    )
+    args = parser.parse_known_args()[0]
+    return args
+
+
+def test_discrete_crr(args=get_args()):
+    # envs
+    env = gym.make(args.task)
+    if args.task == 'CartPole-v0':
+        env.spec.reward_threshold = 190  # lower the goal
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    test_envs = DummyVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    test_envs.seed(args.seed)
+    # model
+    actor = Net(args.state_shape, args.action_shape,
+                hidden_sizes=args.hidden_sizes, device=args.device,
+                softmax=False)
+    critic = Net(args.state_shape, args.action_shape,
+                 hidden_sizes=args.hidden_sizes, device=args.device,
+                 softmax=False)
+    optim = torch.optim.Adam(list(actor.parameters()) + list(critic.parameters()),
+                             lr=args.lr)
+
+    policy = DiscreteCRRPolicy(
+        actor, critic, optim, args.gamma,
+        target_update_freq=args.target_update_freq,
+    ).to(args.device)
+    # buffer
+    assert os.path.exists(args.load_buffer_name), \
+        "Please run test_dqn.py first to get expert's data buffer."
+    buffer = pickle.load(open(args.load_buffer_name, "rb"))
+
+    # collector
+    test_collector = Collector(policy, test_envs, exploration_noise=True)
+
+    log_path = os.path.join(args.logdir, args.task, 'discrete_cql')
+    writer = SummaryWriter(log_path)
+    logger = BasicLogger(writer)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        return mean_rewards >= env.spec.reward_threshold
+
+    result = offline_trainer(
+        policy, buffer, test_collector,
+        args.epoch, args.update_per_epoch, args.test_num, args.batch_size,
+        stop_fn=stop_fn, save_fn=save_fn, logger=logger)
+
+    assert stop_fn(result['best_reward'])
+
+    if __name__ == '__main__':
+        pprint.pprint(result)
+        # Let's watch its performance!
+        env = gym.make(args.task)
+        policy.eval()
+        collector = Collector(policy, env)
+        result = collector.collect(n_episode=1, render=args.render)
+        rews, lens = result["rews"], result["lens"]
+        print(f"Final reward: {rews.mean()}, length: {lens.mean()}")
+
+
+if __name__ == "__main__":
+    test_discrete_crr(get_args())
diff --git a/test/discrete/test_qrdqn_il_cql.py b/test/discrete/test_qrdqn_il_cql.py
index eb7de42..7a782dd 100644
--- a/test/discrete/test_qrdqn_il_cql.py
+++ b/test/discrete/test_qrdqn_il_cql.py
@@ -71,7 +71,7 @@ def test_discrete_cql(args=get_args()):
     ).to(args.device)
     # buffer
     assert os.path.exists(args.load_buffer_name), \
-        "Please run test_dqn.py first to get expert's data buffer."
+        "Please run test_qrdqn.py first to get expert's data buffer."
     buffer = pickle.load(open(args.load_buffer_name, "rb"))
 
     # collector
diff --git a/tianshou/policy/__init__.py b/tianshou/policy/__init__.py
index 30b1af9..54f0f4a 100644
--- a/tianshou/policy/__init__.py
+++ b/tianshou/policy/__init__.py
@@ -15,6 +15,7 @@ from tianshou.policy.modelfree.discrete_sac import DiscreteSACPolicy
 from tianshou.policy.imitation.base import ImitationPolicy
 from tianshou.policy.imitation.discrete_bcq import DiscreteBCQPolicy
 from tianshou.policy.imitation.discrete_cql import DiscreteCQLPolicy
+from tianshou.policy.imitation.discrete_crr import DiscreteCRRPolicy
 from tianshou.policy.modelbased.psrl import PSRLPolicy
 from tianshou.policy.multiagent.mapolicy import MultiAgentPolicyManager
 
@@ -37,6 +38,7 @@ __all__ = [
     "ImitationPolicy",
     "DiscreteBCQPolicy",
     "DiscreteCQLPolicy",
+    "DiscreteCRRPolicy",
     "PSRLPolicy",
     "MultiAgentPolicyManager",
 ]
diff --git a/tianshou/policy/imitation/discrete_crr.py b/tianshou/policy/imitation/discrete_crr.py
new file mode 100644
index 0000000..f5b203f
--- /dev/null
+++ b/tianshou/policy/imitation/discrete_crr.py
@@ -0,0 +1,123 @@
+import torch
+from copy import deepcopy
+from typing import Any, Dict
+import torch.nn.functional as F
+from torch.distributions import Categorical
+
+from tianshou.policy.modelfree.pg import PGPolicy
+from tianshou.data import Batch, to_torch, to_torch_as
+
+
+class DiscreteCRRPolicy(PGPolicy):
+    r"""Implementation of discrete Critic Regularized Regression. arXiv:2006.15134.
+
+    :param torch.nn.Module actor: the actor network following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> logits)
+    :param torch.nn.Module critic: the action-value critic (i.e., Q function)
+        network. (s -> Q(s, \*))
+    :param torch.optim.Optimizer optim: a torch.optim for optimizing the model.
+    :param float discount_factor: in [0, 1]. Default to 0.99.
+    :param str policy_improvement_mode: type of the weight function f. Possible
+        values: "binary"/"exp"/"all". Default to "exp".
+    :param float ratio_upper_bound: when policy_improvement_mode is "exp", the value
+        of the exp function is upper-bounded by this parameter. Default to 20.
+    :param float beta: when policy_improvement_mode is "exp", this is the denominator
+        of the exp function. Default to 1.
+    :param float min_q_weight: weight for CQL loss/regularizer. Default to 10.
+    :param int target_update_freq: the target network update frequency (0 if
+        you do not use the target network). Default to 0.
+    :param bool reward_normalization: normalize the reward to Normal(0, 1).
+        Default to False.
+
+    .. seealso::
+        Please refer to :class:`~tianshou.policy.PGPolicy` for more detailed
+        explanation.
+    """
+
+    def __init__(
+        self,
+        actor: torch.nn.Module,
+        critic: torch.nn.Module,
+        optim: torch.optim.Optimizer,
+        discount_factor: float = 0.99,
+        policy_improvement_mode: str = "exp",
+        ratio_upper_bound: float = 20.0,
+        beta: float = 1.0,
+        min_q_weight: float = 10.0,
+        target_update_freq: int = 0,
+        reward_normalization: bool = False,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(
+            actor,
+            optim,
+            lambda x: Categorical(logits=x),  # type: ignore
+            discount_factor,
+            reward_normalization,
+            **kwargs,
+        )
+        self.critic = critic
+        self._target = target_update_freq > 0
+        self._freq = target_update_freq
+        self._iter = 0
+        if self._target:
+            self.actor_old = deepcopy(self.actor)
+            self.actor_old.eval()
+            self.critic_old = deepcopy(self.critic)
+            self.critic_old.eval()
+        else:
+            self.actor_old = self.actor
+            self.critic_old = self.critic
+        assert policy_improvement_mode in ["exp", "binary", "all"]
+        self._policy_improvement_mode = policy_improvement_mode
+        self._ratio_upper_bound = ratio_upper_bound
+        self._beta = beta
+        self._min_q_weight = min_q_weight
+
+    def sync_weight(self) -> None:
+        self.actor_old.load_state_dict(self.actor.state_dict())  # type: ignore
+        self.critic_old.load_state_dict(self.critic.state_dict())  # type: ignore
+
+    def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:  # type: ignore
+        if self._target and self._iter % self._freq == 0:
+            self.sync_weight()
+        self.optim.zero_grad()
+        q_t, _ = self.critic(batch.obs)
+        act = to_torch(batch.act, dtype=torch.long, device=q_t.device)
+        qa_t = q_t.gather(1, act.unsqueeze(1))
+        # Critic loss
+        with torch.no_grad():
+            target_a_t, _ = self.actor_old(batch.obs_next)
+            target_m = Categorical(logits=target_a_t)
+            q_t_target, _ = self.critic_old(batch.obs_next)
+            rew = to_torch_as(batch.rew, q_t_target)
+            expected_target_q = (q_t_target * target_m.probs).sum(-1, keepdim=True)
+            expected_target_q[batch.done > 0] = 0.0
+            target = rew.unsqueeze(1) + self._gamma * expected_target_q
+        critic_loss = 0.5 * F.mse_loss(qa_t, target)
+        # Actor loss
+        a_t, _ = self.actor(batch.obs)
+        m = Categorical(logits=a_t)
+        expected_policy_q = (q_t * m.probs).sum(-1, keepdim=True)
+        advantage = qa_t - expected_policy_q
+        if self._policy_improvement_mode == "binary":
+            actor_loss_coef = (advantage > 0).float()
+        elif self._policy_improvement_mode == "exp":
+            actor_loss_coef = (
+                (advantage / self._beta).exp().clamp(0, self._ratio_upper_bound)
+            )
+        else:
+            actor_loss_coef = 1.0  # effectively behavior cloning
+        actor_loss = (-m.log_prob(act) * actor_loss_coef).mean()
+        # CQL loss/regularizer
+        min_q_loss = (q_t.logsumexp(1) - qa_t).mean()
+        loss = actor_loss + critic_loss + self._min_q_weight * min_q_loss
+        loss.backward()
+        self.optim.step()
+        self._iter += 1
+        return {
+            "loss": loss.item(),
+            "loss/actor": actor_loss.item(),
+            "loss/critic": critic_loss.item(),
+            "loss/cql": min_q_loss.item(),
+        }