diff --git a/paddle/phi/kernels/funcs/elementwise_functor.h b/paddle/phi/kernels/funcs/elementwise_functor.h
index bf119e27309f5b..e44b8e4eed218b 100644
--- a/paddle/phi/kernels/funcs/elementwise_functor.h
+++ b/paddle/phi/kernels/funcs/elementwise_functor.h
@@ -22,7 +22,7 @@ limitations under the License. */
 #include "paddle/phi/core/enforce.h"
 #if defined(__xpu__)
 #include <xpu/runtime.h>
-
+#include <type_traits>
 #include "xpu/kernel/math_xpu2.h"  // pow()
 #endif
 #include "paddle/phi/common/amp_type_traits.h"
@@ -467,9 +467,40 @@ struct MultiplyGradXYFunctor<ComplexType<InT>, ComplexType<OutT>> {
 };
 
 // Maximum
-template <typename T>
+template <typename T, typename Enable = void>
 struct MaximumFunctor {
   inline HOSTDEVICE T operator()(const T a, const T b) const {
+    if constexpr ((std::is_floating_point_v<T>)&&(
+                      !(std::is_same_v<T, int32_t> ||
+                        std::is_same_v<T, int64_t>))) {
+#if defined(__CUDACC__) || defined(__HIPCC__)
+      if (::isnan(a)) {
+        return a;
+      }
+      if (::isnan(b)) {
+        return b;
+      }
+#else
+      if (std::isnan(a)) {
+        return a;
+      }
+      if (std::isnan(b)) {
+        return b;
+      }
+#endif
+    }
+    return a > b ? a : b;
+  }
+};
+
+template <typename T>
+struct MaximumFunctor<
+    T,
+    typename std::enable_if<std::is_same_v<T, phi::dtype::bfloat16> ||
+                            std::is_same_v<T, phi::dtype::float16>>::type> {
+  inline HOSTDEVICE T operator()(const T a, const T b) const {
+    if (phi::dtype::isnan(a)) return a;
+    if (phi::dtype::isnan(b)) return b;
     return a > b ? a : b;
   }
 };
@@ -509,12 +540,44 @@ struct MaxGradXYFunctor {
 };
 
 // Minimum
-template <typename T>
+template <typename T, typename Enable = void>
 struct MinimumFunctor {
   inline HOSTDEVICE T operator()(const T a, const T b) const {
+    if constexpr (std::is_floating_point_v<T> &&
+                  (!(std::is_same_v<T, int32_t> ||
+                     std::is_same_v<T, int64_t>))) {
+#if defined(__CUDACC__) || defined(__HIPCC__)
+      if (::isnan(a)) {
+        return a;
+      }
+      if (::isnan(b)) {
+        return b;
+      }
+#else
+      if (std::isnan(a)) {
+        return a;
+      }
+      if (std::isnan(b)) {
+        return b;
+      }
+#endif
+    }
     return a < b ? a : b;
   }
 };
+
+template <typename T>
+struct MinimumFunctor<
+    T,
+    typename std::enable_if<std::is_same_v<T, phi::dtype::bfloat16> ||
+                            std::is_same_v<T, phi::dtype::float16>>::type> {
+  inline HOSTDEVICE T operator()(const T a, const T b) const {
+    if (phi::dtype::isnan(a)) return a;
+    if (phi::dtype::isnan(b)) return b;
+    return a < b ? a : b;
+  }
+};
+
 template <typename T>
 struct MinGradXFunctor {
   inline HOSTDEVICE T operator()(const T x, const T y, const T dout) const {
diff --git a/test/legacy_test/test_maximum_op.py b/test/legacy_test/test_maximum_op.py
index 1388d720e1b35b..6fa1e356eedba6 100644
--- a/test/legacy_test/test_maximum_op.py
+++ b/test/legacy_test/test_maximum_op.py
@@ -15,6 +15,7 @@
 import unittest
 
 import numpy as np
+from utils import dygraph_guard, static_guard
 
 import paddle
 from paddle.base import core
@@ -34,10 +35,22 @@ def setUp(self):
         self.input_b = np.array([2, np.inf, -np.inf]).astype('int64')
         self.input_c = np.array([4, 1, 3]).astype('int64')
 
+        self.input_nan_a = np.array([0, np.nan, np.nan]).astype('float32')
+        self.input_nan_b = np.array([0, 1, 2]).astype('float32')
+
         self.np_expected1 = np.maximum(self.input_x, self.input_y)
         self.np_expected2 = np.maximum(self.input_x, self.input_z)
         self.np_expected3 = np.maximum(self.input_a, self.input_c)
         self.np_expected4 = np.maximum(self.input_b, self.input_c)
+        self.np_expected_nan_aa = np.maximum(
+            self.input_nan_a, self.input_nan_a
+        )  # maximum(Nan, Nan)
+        self.np_expected_nan_ab = np.maximum(
+            self.input_nan_a, self.input_nan_b
+        )  # maximum(Nan, Num)
+        self.np_expected_nan_ba = np.maximum(
+            self.input_nan_b, self.input_nan_a
+        )  # maximum(Num, Nan)
 
     def test_static_api(self):
         paddle.enable_static()
@@ -164,6 +177,83 @@ def test_equal_tensors(self):
             1e-2,
         )
 
+    @unittest.skipIf(
+        core.is_compiled_with_xpu(),
+        "XPU need fix the bug",
+    )
+    def test_dynamic_nan(self):
+        with dygraph_guard():
+            nan_a = paddle.to_tensor(self.input_nan_a)
+            nan_b = paddle.to_tensor(self.input_nan_b)
+            res = paddle.maximum(nan_a, nan_a)
+            res = res.numpy()
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_aa, rtol=1e-05, equal_nan=True
+            )
+
+            res = paddle.maximum(nan_a, nan_b)
+            res = res.numpy()
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ab, rtol=1e-05, equal_nan=True
+            )
+
+            res = paddle.maximum(nan_b, nan_a)
+            res = res.numpy()
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ba, rtol=1e-05, equal_nan=True
+            )
+
+    @unittest.skipIf(
+        core.is_compiled_with_xpu(),
+        "XPU need fix the bug",
+    )
+    def test_static_nan(self):
+        with static_guard():
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                data_a = paddle.static.data("a", shape=[3], dtype="float32")
+                data_b = paddle.static.data("b", shape=[3], dtype="float32")
+                result_max = paddle.maximum(data_a, data_b)
+                exe = paddle.static.Executor(self.place)
+                (res,) = exe.run(
+                    feed={"a": self.input_nan_a, "b": self.input_nan_a},
+                    fetch_list=[result_max],
+                )
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_aa, rtol=1e-05, equal_nan=True
+            )
+
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                data_a = paddle.static.data("a", shape=[3], dtype="float32")
+                data_b = paddle.static.data("b", shape=[3], dtype="float32")
+                result_max = paddle.maximum(data_a, data_b)
+                exe = paddle.static.Executor(self.place)
+                (res,) = exe.run(
+                    feed={"a": self.input_nan_a, "b": self.input_nan_b},
+                    fetch_list=[result_max],
+                )
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ab, rtol=1e-05, equal_nan=True
+            )
+
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                data_a = paddle.static.data("a", shape=[3], dtype="float32")
+                data_b = paddle.static.data("b", shape=[3], dtype="float32")
+                result_max = paddle.maximum(data_a, data_b)
+                exe = paddle.static.Executor(self.place)
+                (res,) = exe.run(
+                    feed={"a": self.input_nan_b, "b": self.input_nan_a},
+                    fetch_list=[result_max],
+                )
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ba, rtol=1e-05, equal_nan=True
+            )
+
     def test_0size_input(self):
         numpy_tensor = np.ones([0, 1, 2]).astype("float32")
         paddle_x = paddle.to_tensor(numpy_tensor)
diff --git a/test/legacy_test/test_minimum_op.py b/test/legacy_test/test_minimum_op.py
index c69e3ac29f2d68..f5847a8898e72a 100644
--- a/test/legacy_test/test_minimum_op.py
+++ b/test/legacy_test/test_minimum_op.py
@@ -15,6 +15,7 @@
 import unittest
 
 import numpy as np
+from utils import dygraph_guard, static_guard
 
 import paddle
 from paddle.base import core
@@ -34,10 +35,22 @@ def setUp(self):
         self.input_b = np.array([2, np.inf, -np.inf]).astype('int64')
         self.input_c = np.array([4, 1, 3]).astype('int64')
 
+        self.input_nan_a = np.array([0, np.nan, np.nan]).astype('float32')
+        self.input_nan_b = np.array([0, 1, 2]).astype('float32')
+
         self.np_expected1 = np.minimum(self.input_x, self.input_y)
         self.np_expected2 = np.minimum(self.input_x, self.input_z)
         self.np_expected3 = np.minimum(self.input_a, self.input_c)
         self.np_expected4 = np.minimum(self.input_b, self.input_c)
+        self.np_expected_nan_aa = np.minimum(
+            self.input_nan_a, self.input_nan_a
+        )  # minimum(Nan, Nan)
+        self.np_expected_nan_ab = np.minimum(
+            self.input_nan_a, self.input_nan_b
+        )  # minimum(Nan, Num)
+        self.np_expected_nan_ba = np.minimum(
+            self.input_nan_b, self.input_nan_a
+        )  # minimum(Num, Nan)
 
     def test_static_api(self):
         paddle.enable_static()
@@ -164,6 +177,84 @@ def test_equal_tensors(self):
             1e-2,
         )
 
+    @unittest.skipIf(
+        core.is_compiled_with_xpu(),
+        "XPU need fix the bug",
+    )
+    def test_dynamic_nan(self):
+        with dygraph_guard():
+            nan_a = paddle.to_tensor(self.input_nan_a)
+            nan_b = paddle.to_tensor(self.input_nan_b)
+
+            res = paddle.minimum(nan_a, nan_a)
+            res = res.numpy()
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_aa, rtol=1e-05, equal_nan=True
+            )
+
+            res = paddle.minimum(nan_a, nan_b)
+            res = res.numpy()
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ab, rtol=1e-05, equal_nan=True
+            )
+
+            res = paddle.minimum(nan_b, nan_a)
+            res = res.numpy()
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ba, rtol=1e-05, equal_nan=True
+            )
+
+    @unittest.skipIf(
+        core.is_compiled_with_xpu(),
+        "XPU need fix the bug",
+    )
+    def test_static_nan(self):
+        with static_guard():
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                data_a = paddle.static.data("a", shape=[3], dtype="float32")
+                data_b = paddle.static.data("b", shape=[3], dtype="float32")
+                result_max = paddle.minimum(data_a, data_b)
+                exe = paddle.static.Executor(self.place)
+                (res,) = exe.run(
+                    feed={"a": self.input_nan_a, "b": self.input_nan_a},
+                    fetch_list=[result_max],
+                )
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_aa, rtol=1e-05, equal_nan=True
+            )
+
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                data_a = paddle.static.data("a", shape=[3], dtype="float32")
+                data_b = paddle.static.data("b", shape=[3], dtype="float32")
+                result_max = paddle.minimum(data_a, data_b)
+                exe = paddle.static.Executor(self.place)
+                (res,) = exe.run(
+                    feed={"a": self.input_nan_a, "b": self.input_nan_b},
+                    fetch_list=[result_max],
+                )
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ab, rtol=1e-05, equal_nan=True
+            )
+
+            with paddle.static.program_guard(
+                paddle.static.Program(), paddle.static.Program()
+            ):
+                data_a = paddle.static.data("a", shape=[3], dtype="float32")
+                data_b = paddle.static.data("b", shape=[3], dtype="float32")
+                result_max = paddle.minimum(data_a, data_b)
+                exe = paddle.static.Executor(self.place)
+                (res,) = exe.run(
+                    feed={"a": self.input_nan_b, "b": self.input_nan_a},
+                    fetch_list=[result_max],
+                )
+            np.testing.assert_allclose(
+                res, self.np_expected_nan_ba, rtol=1e-05, equal_nan=True
+            )
+
     def test_0size_input(self):
         numpy_tensor = np.ones([0, 1, 2]).astype("float32")
         paddle_x = paddle.to_tensor(numpy_tensor)