diff --git a/python/paddle/distribution.py b/python/paddle/distribution.py
index 35204affb3fd168b8bd137d78c3413a08885e2bb..a4823c76a364b477519759b0415e96c5e92409b0 100644
--- a/python/paddle/distribution.py
+++ b/python/paddle/distribution.py
@@ -34,7 +34,7 @@ import warnings
 
 from .fluid.data_feeder import convert_dtype, check_variable_and_dtype, check_type, check_dtype
 
-__all__ = ['Distribution', 'Uniform', 'Normal']
+__all__ = ['Distribution', 'Uniform', 'Normal', 'Categorical']
 
 
 class Distribution(object):
@@ -640,3 +640,154 @@ class Normal(Distribution):
         t1 = (t1 * t1)
         return elementwise_add(
             0.5 * var_ratio, 0.5 * (t1 - 1. - nn.log(var_ratio)), name=name)
+
+
+class Categorical(Distribution):
+    """
+    Categorical distribution is a discrete probability distribution that 
+    describes the possible results of a random variable that can take on 
+    one of K possible categories, with the probability of each category 
+    separately specified.
+
+    The probability mass function (pmf) is:
+
+    .. math::
+
+        pmf(k; p_i) = \prod_{i=1}^{k} p_i^{[x=i]}
+
+    In the above equation:
+
+    * :math:`[x=i]` : it evaluates to 1 if :math:`x==i` , 0 otherwise.
+
+    Args:
+        logits(list|numpy.ndarray|Variable): The logits input of categorical distribution. The data type is float32.
+
+    Examples:
+        .. code-block:: python
+
+          import numpy as np
+          from paddle.fluid import layers
+          from paddle.fluid.layers import Categorical
+
+          a_logits_npdata = np.array([-0.602,-0.602], dtype="float32")
+          a_logits_tensor = layers.create_tensor(dtype="float32")
+          layers.assign(a_logits_npdata, a_logits_tensor)
+
+          b_logits_npdata = np.array([-0.102,-0.112], dtype="float32")
+          b_logits_tensor = layers.create_tensor(dtype="float32")
+          layers.assign(b_logits_npdata, b_logits_tensor)
+          
+          a = Categorical(a_logits_tensor)
+          b = Categorical(b_logits_tensor)
+
+          a.entropy()
+          # [0.6931472] with shape: [1]
+
+          b.entropy()
+          # [0.6931347] with shape: [1]
+
+          a.kl_divergence(b)
+          # [1.2516975e-05] with shape: [1]
+
+    """
+
+    def __init__(self, logits, name=None):
+        """
+        Args:
+            logits(list|numpy.ndarray|Variable): The logits input of categorical distribution. The data type is float32.
+        """
+        if not in_dygraph_mode():
+            check_type(logits, 'logits', (np.ndarray, tensor.Variable, list),
+                       'Categorical')
+
+        self.name = name if name is not None else 'Categorical'
+        self.dtype = 'float32'
+
+        if self._validate_args(logits):
+            self.logits = logits
+            self.dtype = convert_dtype(logits.dtype)
+        else:
+            if isinstance(logits, np.ndarray) and str(
+                    logits.dtype) in ['float32', 'float64']:
+                self.dtype = logits.dtype
+            self.logits = self._to_tensor(logits)[0]
+            if self.dtype != convert_dtype(self.logits.dtype):
+                self.logits = tensor.cast(self.logits, dtype=self.dtype)
+
+    def sample(self, shape):
+        """Generate samples of the specified shape.
+
+        Args:
+          shape (list): 1D `int32`. Shape of the generated samples.
+
+        Returns:
+          Tensor: A tensor with prepended dimensions shape.The data type is float32.
+
+        """
+        name = self.name + '_sample'
+        num_samples = np.prod(np.array(shape))
+
+        if in_dygraph_mode():
+            sample_index = core.ops.multinomial(
+                self.logits, 'num_samples', num_samples, 'replacement', True)
+            return nn.reshape(sample_index, shape + [-1])
+
+        check_type(shape, 'shape', (list), 'sample')
+
+        helper = LayerHelper("multinomial", **locals())
+        out = helper.create_variable_for_type_inference(
+            dtype=convert_np_dtype_to_dtype_('int64'))
+        helper.append_op(
+            type='multinomial',
+            inputs={"X": self.logits},
+            outputs={'Out': out},
+            attrs={'num_samples': num_samples,
+                   'replacement': True})
+        return nn.reshape(out, shape + [-1], name=name)
+
+    def kl_divergence(self, other):
+        """The KL-divergence between two Categorical distributions.
+
+        Args:
+            other (Categorical): instance of Categorical. The data type is float32.
+
+        Returns:
+            Variable: kl-divergence between two Categorical distributions.
+
+        """
+        name = self.name + '_kl_divergence'
+        if not in_dygraph_mode():
+            check_type(other, 'other', Categorical, 'kl_divergence')
+
+        logits = self.logits - nn.reduce_max(self.logits, dim=-1, keep_dim=True)
+        other_logits = other.logits - nn.reduce_max(
+            other.logits, dim=-1, keep_dim=True)
+        e_logits = ops.exp(logits)
+        other_e_logits = ops.exp(other_logits)
+        z = nn.reduce_sum(e_logits, dim=-1, keep_dim=True)
+        other_z = nn.reduce_sum(other_e_logits, dim=-1, keep_dim=True)
+        prob = e_logits / z
+        kl = nn.reduce_sum(
+            prob * (logits - nn.log(z) - other_logits + nn.log(other_z)),
+            dim=-1,
+            keep_dim=True,
+            name=name)
+
+        return kl
+
+    def entropy(self):
+        """Shannon entropy in nats.
+
+        Returns:
+          Variable: Shannon entropy of Categorical distribution. The data type is float32.
+
+        """
+        name = self.name + '_entropy'
+        logits = self.logits - nn.reduce_max(self.logits, dim=-1, keep_dim=True)
+        e_logits = ops.exp(logits)
+        z = nn.reduce_sum(e_logits, dim=-1, keep_dim=True)
+        prob = e_logits / z
+        entropy = -1.0 * nn.reduce_sum(
+            prob * (logits - nn.log(z)), dim=-1, keep_dim=True, name=name)
+
+        return entropy