diff --git a/paddle/fluid/framework/generator.cc b/paddle/fluid/framework/generator.cc
index 3ebf09cc7aafefd3c3f8a62150b31ac345302d63..cc2d76a57a940b258a92f2f5a309d161839cb532 100644
--- a/paddle/fluid/framework/generator.cc
+++ b/paddle/fluid/framework/generator.cc
@@ -131,6 +131,11 @@ std::shared_ptr<std::mt19937_64> GetCPURandomEngine(uint64_t seed) {
 phi::Generator::GeneratorState Generator::GetState() {
   std::lock_guard<std::mutex> lock(this->mu_);
   state_.cpu_engine = *engine_;
+  VLOG(4) << "Get Random state: "
+          << "device id: " << (uint64_t)(this->state_.device)
+          << ", current_seed: " << this->state_.current_seed
+          << ", thread_offset: " << this->state_.thread_offset
+          << ", cpu engine: " << *(this->engine_);
   return this->state_;
 }
 
@@ -138,6 +143,11 @@ void Generator::SetState(const phi::Generator::GeneratorState& state) {
   std::lock_guard<std::mutex> lock(this->mu_);
   this->state_ = state;
   this->engine_ = std::make_shared<std::mt19937_64>(state.cpu_engine);
+  VLOG(4) << "Set Random state: "
+          << "device id: " << (uint64_t)(this->state_.device)
+          << ", current_seed: " << this->state_.current_seed
+          << ", thread_offset: " << this->state_.thread_offset
+          << ", cpu engine: " << *(this->engine_);
 }
 
 uint64_t Generator::GetCurrentSeed() {
diff --git a/paddle/fluid/pybind/generator_py.cc b/paddle/fluid/pybind/generator_py.cc
index e456526f8441cb06841b630cc69a4ac72aa91fb2..00ee7b2336849e4f5167bca84644cf1a0fbe619a 100644
--- a/paddle/fluid/pybind/generator_py.cc
+++ b/paddle/fluid/pybind/generator_py.cc
@@ -39,7 +39,38 @@ void BindGenerator(py::module* m_ptr) {
       .def("current_seed",
            [](std::shared_ptr<phi::Generator::GeneratorState>& self) {
              return self->current_seed;
-           });
+           })
+#if defined(PADDLE_WITH_CUDA) || defined(PADDLE_WITH_HIP)
+      // NOTE(shenliang03): Due to the inability to serialize mt19937_64
+      // type, resulting in a problem with precision under the cpu.
+      .def(py::pickle(
+          [](const phi::Generator::GeneratorState& s) {  // __getstate__
+            return py::make_tuple(s.device, s.current_seed, s.thread_offset);
+          },
+          [](py::tuple s) {  // __setstate__
+            if (s.size() != 3)
+              throw std::runtime_error(
+                  "Invalid Random state. Please check the format(device, "
+                  "current_seed, thread_offset).");
+
+            phi::Generator::GeneratorState state;
+            state.device = s[0].cast<std::int64_t>();
+            state.current_seed = s[1].cast<std::uint64_t>();
+            state.thread_offset = s[2].cast<std::uint64_t>();
+
+            std::seed_seq seq({state.current_seed});
+            auto engine = std::make_shared<std::mt19937_64>(seq);
+            state.cpu_engine = *engine;
+            return state;
+          }))
+#endif
+      .def("__str__", [](const phi::Generator::GeneratorState& self) {
+        std::stringstream ostr;
+        ostr << self.device << " " << self.current_seed << " "
+             << self.thread_offset << " " << self.cpu_engine;
+        return ostr.str();
+      });
+
   py::class_<std::mt19937_64>(m, "mt19937_64", "");
   py::class_<framework::Generator, std::shared_ptr<framework::Generator>>(
       m, "Generator")
diff --git a/python/paddle/fluid/tests/unittests/test_cuda_random_seed.py b/python/paddle/fluid/tests/unittests/test_cuda_random_seed.py
index ad854bebd01fcac47e81ed742b48b123fd7f04de..dab8745dbbb0999a10f9f6b9a50da8b48755ac50 100644
--- a/python/paddle/fluid/tests/unittests/test_cuda_random_seed.py
+++ b/python/paddle/fluid/tests/unittests/test_cuda_random_seed.py
@@ -23,6 +23,8 @@ import paddle.fluid as fluid
 import numpy as np
 import paddle
 import paddle.fluid.core as core
+import shutil
+import tempfile
 
 
 @unittest.skipIf(not core.is_compiled_with_cuda(),
@@ -169,6 +171,41 @@ class TestGeneratorSeed(unittest.TestCase):
             np.testing.assert_allclose(out1_res2, out2_res2, rtol=1e-05)
             self.assertTrue(not np.allclose(out1_res2, out1_res1))
 
+    def test_generator_pickle(self):
+        output_dir = tempfile.mkdtemp()
+        random_file = os.path.join(output_dir, "random.pdmodel")
+
+        fluid.enable_dygraph()
+        x0 = paddle.randn([120], dtype="float32")
+
+        st = paddle.get_cuda_rng_state()
+        st_dict = {"random_state": st}
+        print("state: ", st[0])
+
+        paddle.save(st_dict, random_file)
+        x1 = paddle.randn([120], dtype="float32")
+
+        lt_dict = paddle.load(random_file)
+        st = lt_dict["random_state"]
+
+        paddle.set_cuda_rng_state(st)
+        x2 = paddle.randn([120], dtype="float32")
+
+        lt_dict = paddle.load(random_file)
+        st = lt_dict["random_state"]
+        paddle.set_cuda_rng_state(st)
+        x3 = paddle.randn([120], dtype="float32")
+
+        x1_np = x1.numpy()
+        x2_np = x2.numpy()
+        x3_np = x3.numpy()
+
+        print(">>>>>>> gaussian random dygraph state load/save >>>>>>>")
+        np.testing.assert_equal(x1_np, x2_np)
+        np.testing.assert_equal(x1_np, x2_np)
+
+        shutil.rmtree(output_dir)
+
 
 if __name__ == "__main__":
     unittest.main()