diff --git a/python/paddle/fluid/tests/unittests/test_std_layer.py b/python/paddle/fluid/tests/unittests/test_std_layer.py
index df5977eae8809a73a7749bc88e64011f0d2657b7..8f8899f47f7fefac807ea95cbce7261e1543a21c 100644
--- a/python/paddle/fluid/tests/unittests/test_std_layer.py
+++ b/python/paddle/fluid/tests/unittests/test_std_layer.py
@@ -119,5 +119,30 @@ class TestStdError(unittest.TestCase):
             self.assertRaises(TypeError, paddle.std, x)
 
 
+class Testfp16Std(unittest.TestCase):
+    def test_fp16_with_gpu(self):
+        paddle.enable_static()
+        if paddle.fluid.core.is_compiled_with_cuda():
+            place = paddle.CUDAPlace(0)
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                input = np.random.random([12, 14]).astype("float16")
+                x = paddle.static.data(
+                    name="x", shape=[12, 14], dtype="float16"
+                )
+
+                y = paddle.std(x)
+
+                exe = paddle.static.Executor(place)
+                res = exe.run(
+                    paddle.static.default_main_program(),
+                    feed={
+                        "x": input,
+                    },
+                    fetch_list=[y],
+                )
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/python/paddle/tensor/stat.py b/python/paddle/tensor/stat.py
index 35d1a4337b6dfdd6ed5489dbe2b67a7598b1d69a..d3a3ef406728fc3627a5c67aa4570d6251a28489 100644
--- a/python/paddle/tensor/stat.py
+++ b/python/paddle/tensor/stat.py
@@ -119,7 +119,7 @@ def var(x, axis=None, unbiased=True, keepdim=False, name=None):
     Computes the variance of ``x`` along ``axis`` .
 
     Args:
-        x (Tensor): The input Tensor with data type float32, float64.
+        x (Tensor): The input Tensor with data type float16, float32, float64.
         axis (int|list|tuple, optional): The axis along which to perform variance calculations. ``axis`` should be int, list(int) or tuple(int).
 
             - If ``axis`` is a list/tuple of dimension(s), variance is calculated along all element(s) of ``axis`` . ``axis`` or element(s) of ``axis`` should be in range [-D, D), where D is the dimensions of ``x`` .
@@ -145,7 +145,9 @@ def var(x, axis=None, unbiased=True, keepdim=False, name=None):
             # [1.         4.33333333]
     """
     if not in_dygraph_mode():
-        check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'var')
+        check_variable_and_dtype(
+            x, 'x', ['float16', 'float32', 'float64'], 'var'
+        )
 
     u = mean(x, axis, True, name)
     out = paddle.sum(paddle.pow((x - u), 2), axis, keepdim=keepdim, name=name)
@@ -168,7 +170,7 @@ def std(x, axis=None, unbiased=True, keepdim=False, name=None):
     Computes the standard-deviation of ``x`` along ``axis`` .
 
     Args:
-        x (Tensor): The input Tensor with data type float32, float64.
+        x (Tensor): The input Tensor with data type float16, float32, float64.
         axis (int|list|tuple, optional): The axis along which to perform
             standard-deviation calculations. ``axis`` should be int, list(int)
             or tuple(int). If ``axis`` is a list/tuple of dimension(s),
@@ -211,7 +213,9 @@ def std(x, axis=None, unbiased=True, keepdim=False, name=None):
 
     """
     if not in_dygraph_mode():
-        check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'std')
+        check_variable_and_dtype(
+            x, 'x', ['float16', 'float32', 'float64'], 'std'
+        )
     out = var(**locals())
     return paddle.sqrt(out)