diff --git a/python/paddle/fluid/tests/unittests/test_cross_op.py b/python/paddle/fluid/tests/unittests/test_cross_op.py
index 66509a863ab748c9328ef460aa6605d0f8335b4d..8e53a36f0510d95ab4c0e61d61df531ec90dfb3d 100644
--- a/python/paddle/fluid/tests/unittests/test_cross_op.py
+++ b/python/paddle/fluid/tests/unittests/test_cross_op.py
@@ -79,7 +79,7 @@ class TestCrossAPI(unittest.TestCase):
         with program_guard(Program(), Program()):
             x = fluid.layers.data(name='x', shape=[-1, 3])
             y = fluid.layers.data(name='y', shape=[-1, 3])
-            z = paddle.cross(x, y, dim=1)
+            z = paddle.cross(x, y, axis=1)
             exe = fluid.Executor(fluid.CPUPlace())
             res, = exe.run(feed={'x': self.data_x,
                                  'y': self.data_y},
@@ -103,6 +103,14 @@ class TestCrossAPI(unittest.TestCase):
                                [-1.0, -1.0, -1.0]])
         self.assertTrue(np.allclose(expect_out, np.array(res)))
 
+        # case 3:
+        with program_guard(Program(), Program()):
+            x = fluid.data(name="x", shape=[-1, 3], dtype="float32")
+            y = fluid.data(name='y', shape=[-1, 3], dtype='float32')
+
+            y_1 = paddle.cross(x, y, name='result')
+            self.assertEqual(('result' in y_1.name), True)
+
     def test_dygraph_api(self):
         self.input_data()
         # case 1:
@@ -119,7 +127,7 @@ class TestCrossAPI(unittest.TestCase):
         with fluid.dygraph.guard():
             x = fluid.dygraph.to_variable(self.data_x)
             y = fluid.dygraph.to_variable(self.data_y)
-            z = paddle.cross(x, y, dim=1)
+            z = paddle.cross(x, y, axis=1)
             np_z = z.numpy()
         expect_out = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0],
                                [0.0, 0.0, 0.0]])
diff --git a/python/paddle/tensor/linalg.py b/python/paddle/tensor/linalg.py
index f0e1c78f1175032708c9776759c0277ca12fba27..7ec68dc8980a1e57059c1ee2f01990250d7dabc8 100644
--- a/python/paddle/tensor/linalg.py
+++ b/python/paddle/tensor/linalg.py
@@ -583,66 +583,69 @@ def t(input, name=None):
     return out
 
 
-def cross(input, other, dim=None):
+def cross(x, y, axis=None, name=None):
     """
 	:alias_main: paddle.cross
 	:alias: paddle.cross,paddle.tensor.cross,paddle.tensor.linalg.cross
 
-    Returns the cross product of vectors in dimension `dim` of the `input` and `other` tensor. 
-    Inputs must have the same shape, and the size of their dim-th dimension should be equla to 3. 
-    If `dim` is not given, it defaults to the first dimension found with the size 3.
+    Computes the cross product between two tensors along an axis.
+    Inputs must have the same shape, and the length of their axes should be equal to 3.
+    If `axis` is not given, it defaults to the first axis found with the length 3.
     
     Args:
-        input (Variable): The first input tensor variable.
-        other (Variable): The second input tensor variable.
-        dim (int): The dimension to take the cross-product in.
+        x (Variable): The first input tensor variable.
+        y (Variable): The second input tensor variable.
+        axis (int, optional): The axis along which to compute the cross product. It defaults to the first axis found with the length 3.
+        name (str, optional): The default value is None.  Normally there is no need for
+            user to set this property.  For more information, please refer to :ref:`api_guide_Name`
 
     Returns:
-        Variable: A Tensor with same data type as `input`.
+        Variable: A Tensor with same data type as `x`.
         
     Examples:
         .. code-block:: python
             import paddle
-            import paddle.fluid as fluid
+            from paddle.imperative import to_variable
             import numpy as np
 
+            paddle.enable_imperative()
+
             data_x = np.array([[1.0, 1.0, 1.0],
                                [2.0, 2.0, 2.0],
                                [3.0, 3.0, 3.0]])
             data_y = np.array([[1.0, 1.0, 1.0],
                                [1.0, 1.0, 1.0],
                                [1.0, 1.0, 1.0]])
-
-            with fluid.dygraph.guard():
-                x = fluid.dygraph.to_variable(data_x)
-                y = fluid.dygraph.to_variable(data_y)
-                out_z1 = paddle.cross(x, y)
-                print(out_z1.numpy())
-                #[[-1. -1. -1.]
-                # [ 2.  2.  2.]
-                # [-1. -1. -1.]]
-                out_z2 = paddle.cross(x, y, dim=1)
-                print(out_z2.numpy())
-                #[[0. 0. 0.]
-                # [0. 0. 0.]
-                # [0. 0. 0.]]
+            x = to_variable(data_x)
+            y = to_variable(data_y)
+
+            z1 = paddle.cross(x, y)
+            print(z1.numpy())
+            # [[-1. -1. -1.]
+            #  [ 2.  2.  2.]
+            #  [-1. -1. -1.]]
+
+            z2 = paddle.cross(x, y, axis=1)
+            print(z2.numpy())
+            # [[0. 0. 0.]
+            #  [0. 0. 0.]
+            #  [0. 0. 0.]]
     """
-    helper = LayerHelper("cross", **locals())
     if in_dygraph_mode():
-        if dim:
-            return core.ops.cross(input, other, 'dim', dim)
+        if axis:
+            return core.ops.cross(x, y, 'dim', axis)
         else:
-            return core.ops.cross(input, other)
+            return core.ops.cross(x, y)
 
-    out = helper.create_variable_for_type_inference(input.dtype)
+    helper = LayerHelper("cross", **locals())
+    out = helper.create_variable_for_type_inference(x.dtype)
     attrs = dict()
-    if dim:
-        attrs['dim'] = dim
+    attrs['dim'] = axis
 
     helper.append_op(
         type='cross',
-        inputs={'X': input,
-                'Y': other},
+        inputs={'X': x,
+                'Y': y},
         outputs={'Out': out},
         attrs=attrs)
     return out