diff --git a/python/paddle/complex/tensor/__init__.py b/python/paddle/complex/tensor/__init__.py
index d1726384d1be85eda21983a3939f7e4bde2eb807..dc5cb35962018cbbb9f64b3ae275d36b95206893 100644
--- a/python/paddle/complex/tensor/__init__.py
+++ b/python/paddle/complex/tensor/__init__.py
@@ -14,8 +14,11 @@
 
 from . import math
 from . import manipulation
+from . import linalg
 from .math import *
 from .manipulation import *
+from .linalg import *
 
-__all__ = math.__all__ + []
+__all__ = math.__all__
 __all__ += manipulation.__all__
+__all__ += linalg.__all__
diff --git a/python/paddle/complex/tensor/linalg.py b/python/paddle/complex/tensor/linalg.py
new file mode 100644
index 0000000000000000000000000000000000000000..99c0ca5fbfab32c1581878f02db10d3338a507c8
--- /dev/null
+++ b/python/paddle/complex/tensor/linalg.py
@@ -0,0 +1,75 @@
+#  Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserve.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# 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 ..helper import is_complex, is_real, complex_variable_exists
+from ...fluid.framework import ComplexVariable
+from ...fluid import layers
+
+__all__ = ['matmul', ]
+
+
+def matmul(x, y, transpose_x=False, transpose_y=False, alpha=1.0, name=None):
+    """
+    Applies matrix multiplication to two complex number tensors. See the 
+    detailed description in :ref:`api_fluid_layers_matmul`.
+
+    Args:
+        x (ComplexVariable|Variable): The first input, can be a ComplexVariable 
+            with data type complex32 or complex64, or a Variable with data type 
+            float32 or float64.
+        y (ComplexVariable|Variable): The second input, can be a ComplexVariable 
+            with data type complex32 or complex64, or a Variable with data type 
+            float32 or float64.
+        transpose_x (bool): Whether to transpose :math:`x` before multiplication.
+        transpose_y (bool): Whether to transpose :math:`y` before multiplication.
+        alpha (float): The scale of output. Default 1.0.
+        name(str|None): A name for this layer(optional). If set None, the layer
+            will be named automatically.
+   
+    Returns:
+        ComplexVariable: The product result, with the same data type as inputs.
+
+    Examples:
+        .. code-block:: python
+
+            import numpy as np
+            import paddle
+            import paddle.fluid.dygraph as dg
+            with dg.guard():
+                x = np.array([[1.0 + 1j, 2.0 + 1j], [3.0+1j, 4.0+1j]])
+                y = np.array([1.0 + 1j, 1.0 + 1j])
+                x_var = dg.to_variable(x)
+                y_var = dg.to_variable(y)
+                result = paddle.complex.matmul(x_var, y_var)
+                print(result.numpy())
+                # [1.+5.j 5.+9.j]         
+    """
+    # x = a + bi, y = c + di
+    # mm(x, y) = mm(a, c) - mm(b, d) + (mm(a, d) + mm(b, c))i
+    complex_variable_exists([x, y], "matmul")
+    a, b = (x.real, x.imag) if is_complex(x) else (x, None)
+    c, d = (y.real, y.imag) if is_complex(y) else (y, None)
+    ac = layers.matmul(a, c, transpose_x, transpose_y, alpha, name)
+    if is_real(b) and is_real(d):
+        bd = layers.matmul(b, d, transpose_x, transpose_y, alpha, name)
+        real = ac - bd
+        imag = layers.matmul(a, d, transpose_x, transpose_y, alpha, name) + \
+               layers.matmul(b, c, transpose_x, transpose_y, alpha, name)
+    elif is_real(b):
+        real = ac
+        imag = layers.matmul(b, c, transpose_x, transpose_y, alpha, name)
+    else:
+        real = ac
+        imag = layers.matmul(a, d, transpose_x, transpose_y, alpha, name)
+    return ComplexVariable(real, imag)
diff --git a/python/paddle/complex/tensor/manipulation.py b/python/paddle/complex/tensor/manipulation.py
index c7201ea5de8fcb7c623c9f291621f9af3f57b20b..18545ad3abab8a5c1f900e54329e97a5416f772e 100644
--- a/python/paddle/complex/tensor/manipulation.py
+++ b/python/paddle/complex/tensor/manipulation.py
@@ -17,7 +17,10 @@ from ..helper import is_complex, is_real, complex_variable_exists
 from ...fluid.framework import ComplexVariable
 from ...fluid import layers
 
-__all__ = ['reshape', ]
+__all__ = [
+    'reshape',
+    'transpose',
+]
 
 
 def reshape(x, shape, inplace=False, name=None):
@@ -104,3 +107,39 @@ def reshape(x, shape, inplace=False, name=None):
     out_real = fluid.layers.reshape(x.real, shape, inplace=inplace, name=name)
     out_imag = fluid.layers.reshape(x.imag, shape, inplace=inplace, name=name)
     return ComplexVariable(out_real, out_imag)
+
+
+def transpose(x, perm, name=None):
+    """
+    Permute the data dimensions for complex number :attr:`input` according to `perm`.
+
+    See :ref:`api_fluid_layers_transpose` for the real number API.
+
+    Args:
+        x (ComplexVariable): The input n-D ComplexVariable with data type
+            complex64 or complex128.
+        perm (list): Permute the input according to the value of perm.
+        name (str): The name of this layer. It is optional.
+
+    Returns:
+        ComplexVariable: A transposed n-D ComplexVariable, with the same data type as :attr:`input`.
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            import numpy as np
+            import paddle.fluid.dygraph as dg
+
+            with dg.guard():
+                a = np.array([[1.0 + 1.0j, 2.0 + 1.0j], [3.0+1.0j, 4.0+1.0j]])
+                x = dg.to_variable(a)
+                y = paddle.complex.transpose(x, [1, 0])
+                print(y.numpy())
+                # [[1.+1.j 3.+1.j]
+                #  [2.+1.j 4.+1.j]]
+    """
+    complex_variable_exists([x], "transpose")
+    real = layers.transpose(x.real, perm, name)
+    imag = layers.transpose(x.imag, perm, name)
+    return ComplexVariable(real, imag)
diff --git a/python/paddle/fluid/framework.py b/python/paddle/fluid/framework.py
index 564fc1fd5adf26547d59e9d947a6935eda0ebb27..5482e6e2f2b35ae8df6a1aaed822bebbf943ab45 100644
--- a/python/paddle/fluid/framework.py
+++ b/python/paddle/fluid/framework.py
@@ -1644,10 +1644,9 @@ class ComplexVariable(object):
     holding the real part and imaginary part of complex numbers respectively.
     
     **Notes**:
-        **The constructor of Variable should not be invoked directly.**
+        **The constructor of ComplexVariable should not be invoked directly.**
 
-        **Only support dygraph mode at present. Please use** :ref:`api_fluid_dygraph_to_variable` **
-          to create a dygraph ComplexVariable with complex number data.**
+        **Only support dygraph mode at present. Please use** :ref:`api_fluid_dygraph_to_variable` **to create a dygraph ComplexVariable with complex number data.**
 
     Args:
         real (Variable): The Variable holding real-part data.
diff --git a/python/paddle/fluid/tests/unittests/test_complex_matmul.py b/python/paddle/fluid/tests/unittests/test_complex_matmul.py
new file mode 100644
index 0000000000000000000000000000000000000000..90d50bdfb27ab9c050e8a3baaeb68c7cc95b725a
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_complex_matmul.py
@@ -0,0 +1,62 @@
+#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# 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.
+
+import unittest
+import paddle
+import numpy as np
+import paddle.fluid as fluid
+import paddle.fluid.dygraph as dg
+
+
+class TestComplexMatMulLayer(unittest.TestCase):
+    def setUp(self):
+        self._places = [fluid.CPUPlace()]
+        if fluid.core.is_compiled_with_cuda():
+            self._places.append(fluid.CUDAPlace(0))
+
+    def compare(self, x, y):
+        for place in self._places:
+            with dg.guard(place):
+                x_var = dg.to_variable(x)
+                y_var = dg.to_variable(y)
+                result = paddle.complex.matmul(x_var, y_var)
+        np_result = np.matmul(x, y)
+        self.assertTrue(np.allclose(result.numpy(), np_result))
+
+    def test_complex_xy(self):
+        x = np.random.random(
+            (2, 3, 4, 5)).astype("float32") + 1J * np.random.random(
+                (2, 3, 4, 5)).astype("float32")
+        y = np.random.random(
+            (2, 3, 5, 4)).astype("float32") + 1J * np.random.random(
+                (2, 3, 5, 4)).astype("float32")
+        self.compare(x, y)
+
+    def test_complex_x(self):
+        x = np.random.random(
+            (2, 3, 4, 5)).astype("float32") + 1J * np.random.random(
+                (2, 3, 4, 5)).astype("float32")
+        y = np.random.random((2, 3, 5, 4)).astype("float32")
+        self.compare(x, y)
+
+    def test_complex_y(self):
+        x = np.random.random((2, 3, 4, 5)).astype("float32")
+        y = np.random.random(
+            (2, 3, 5, 4)).astype("float32") + 1J * np.random.random(
+                (2, 3, 5, 4)).astype("float32")
+        self.compare(x, y)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_complex_transpose.py b/python/paddle/fluid/tests/unittests/test_complex_transpose.py
new file mode 100644
index 0000000000000000000000000000000000000000..e31cb9e7051b47cd5d418cb83b9e074adae88cdb
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_complex_transpose.py
@@ -0,0 +1,42 @@
+#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# 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.
+
+import unittest
+import paddle
+import numpy as np
+import paddle.fluid as fluid
+import paddle.fluid.dygraph as dg
+
+
+class TestComplexTransposeLayer(unittest.TestCase):
+    def setUp(self):
+        self._places = [fluid.CPUPlace()]
+        if fluid.core.is_compiled_with_cuda():
+            self._places.append(fluid.CUDAPlace(0))
+
+    def test_identity(self):
+        data = np.random.random(
+            (2, 3, 4, 5)).astype("float32") + 1J * np.random.random(
+                (2, 3, 4, 5)).astype("float32")
+        perm = [3, 2, 0, 1]
+        np_trans = np.transpose(data, perm)
+        for place in self._places:
+            with dg.guard(place):
+                var = dg.to_variable(data)
+                trans = paddle.complex.transpose(var, perm=perm)
+        self.assertTrue(np.allclose(trans.numpy(), np_trans))
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_complex_variable.py b/python/paddle/fluid/tests/unittests/test_complex_variable.py
index d9b159aa9304b70d47fea0b92e178589a6ebba90..ee69be1d0e3862fc0720cd63efcbeeb8255a95df 100644
--- a/python/paddle/fluid/tests/unittests/test_complex_variable.py
+++ b/python/paddle/fluid/tests/unittests/test_complex_variable.py
@@ -1,4 +1,4 @@
-#   Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
+#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.