diff --git a/python/paddle/distribution/multivariate_normal.py b/python/paddle/distribution/multivariate_normal.py
index 55e6a3cc7f325..9f5f27931d1e8 100644
--- a/python/paddle/distribution/multivariate_normal.py
+++ b/python/paddle/distribution/multivariate_normal.py
@@ -11,13 +11,20 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+from __future__ import annotations
 
 import math
 from collections.abc import Sequence
+from typing import TYPE_CHECKING
 
 import paddle
+from paddle.base.data_feeder import convert_dtype
 from paddle.distribution import distribution
 
+if TYPE_CHECKING:
+    from paddle import Tensor
+    from paddle._typing.dtype_like import _DTypeLiteral
+
 
 class MultivariateNormal(distribution.Distribution):
     r"""The Multivariate Normal distribution is a type multivariate continuous distribution defined on the real set, with parameter: `loc` and any one
@@ -40,11 +47,11 @@ class MultivariateNormal(distribution.Distribution):
     Args:
         loc(int|float|Tensor): The mean of Multivariate Normal distribution. If the input data type is int or float, the data type of `loc` will be
             convert to a 1-D Tensor the paddle global default dtype.
-        covariance_matrix(Tensor): The covariance matrix of Multivariate Normal distribution. The data type of `covariance_matrix` will be convert
+        covariance_matrix(Tensor|None): The covariance matrix of Multivariate Normal distribution. The data type of `covariance_matrix` will be convert
             to be the same as the type of loc.
-        precision_matrix(Tensor): The inverse of the covariance matrix. The data type of `precision_matrix` will be convert to be the same as the
+        precision_matrix(Tensor|None): The inverse of the covariance matrix. The data type of `precision_matrix` will be convert to be the same as the
             type of loc.
-        scale_tril(Tensor): The cholesky decomposition (lower triangular matrix) of the covariance matrix. The data type of `scale_tril` will be
+        scale_tril(Tensor|None): The cholesky decomposition (lower triangular matrix) of the covariance matrix. The data type of `scale_tril` will be
             convert to be the same as the type of loc.
 
     Examples:
@@ -85,18 +92,24 @@ class MultivariateNormal(distribution.Distribution):
             1.55541301)
     """
 
+    loc: Tensor
+    covariance_matrix: Tensor | None
+    precision_matrix: Tensor | None
+    scale_tril: Tensor | None
+    dtype: _DTypeLiteral
+
     def __init__(
         self,
-        loc,
-        covariance_matrix=None,
-        precision_matrix=None,
-        scale_tril=None,
+        loc: float | Tensor,
+        covariance_matrix: Tensor | None = None,
+        precision_matrix: Tensor | None = None,
+        scale_tril: Tensor | None = None,
     ):
         self.dtype = paddle.get_default_dtype()
         if isinstance(loc, (float, int)):
             loc = paddle.to_tensor([loc], dtype=self.dtype)
         else:
-            self.dtype = loc.dtype
+            self.dtype = convert_dtype(loc.dtype)
         if loc.dim() < 1:
             loc = loc.reshape((1,))
         self.covariance_matrix = None
@@ -172,7 +185,7 @@ def __init__(
         super().__init__(batch_shape, event_shape)
 
     @property
-    def mean(self):
+    def mean(self) -> Tensor:
         """Mean of Multivariate Normal distribution.
 
         Returns:
@@ -181,7 +194,7 @@ def mean(self):
         return self.loc
 
     @property
-    def variance(self):
+    def variance(self) -> Tensor:
         """Variance of Multivariate Normal distribution.
 
         Returns:
@@ -193,7 +206,7 @@ def variance(self):
             .expand(self._batch_shape + self._event_shape)
         )
 
-    def sample(self, shape=()):
+    def sample(self, shape: Sequence[int] = ()) -> Tensor:
         """Generate Multivariate Normal samples of the specified shape. The final shape would be ``sample_shape + batch_shape + event_shape``.
 
         Args:
@@ -205,7 +218,7 @@ def sample(self, shape=()):
         with paddle.no_grad():
             return self.rsample(shape)
 
-    def rsample(self, shape=()):
+    def rsample(self, shape: Sequence[int] = ()) -> Tensor:
         """Generate Multivariate Normal samples of the specified shape. The final shape would be ``sample_shape + batch_shape + event_shape``.
 
         Args:
@@ -222,7 +235,7 @@ def rsample(self, shape=()):
             self._unbroadcasted_scale_tril, eps.unsqueeze(-1)
         ).squeeze(-1)
 
-    def log_prob(self, value):
+    def log_prob(self, value: Tensor) -> Tensor:
         """Log probability density function.
 
         Args:
@@ -245,7 +258,7 @@ def log_prob(self, value):
             - half_log_det
         )
 
-    def prob(self, value):
+    def prob(self, value: Tensor) -> Tensor:
         """Probability density function.
 
         Args:
@@ -256,7 +269,7 @@ def prob(self, value):
         """
         return paddle.exp(self.log_prob(value))
 
-    def entropy(self):
+    def entropy(self) -> Tensor:
         r"""Shannon entropy in nats.
 
         The entropy is
@@ -286,7 +299,7 @@ def entropy(self):
         else:
             return H.expand(self._batch_shape)
 
-    def kl_divergence(self, other):
+    def kl_divergence(self, other: MultivariateNormal) -> Tensor:
         r"""The KL-divergence between two poisson distributions with the same `batch_shape` and `event_shape`.
 
         The probability density function (pdf) is
@@ -344,7 +357,7 @@ def kl_divergence(self, other):
         )
 
 
-def precision_to_scale_tril(P):
+def precision_to_scale_tril(P: Tensor) -> Tensor:
     """Convert precision matrix to scale tril matrix
 
     Args:
@@ -363,7 +376,7 @@ def precision_to_scale_tril(P):
     return L
 
 
-def batch_mahalanobis(bL, bx):
+def batch_mahalanobis(bL: Tensor, bx: Tensor) -> Tensor:
     r"""
     Computes the squared Mahalanobis distance of the Multivariate Normal distribution with cholesky decomposition of the covariance matrix.
     Accepts batches for both bL and bx.