diff --git a/paddle/fluid/operators/cholesky_op.cu b/paddle/fluid/operators/cholesky_op.cu
index c44299686516e968692fe146a5c324c7f1fa83d2..530147609fe1e47320a1cbd9223ccdfb82ba7e7a 100644
--- a/paddle/fluid/operators/cholesky_op.cu
+++ b/paddle/fluid/operators/cholesky_op.cu
@@ -63,7 +63,6 @@ class CholeskyGPUKernel : public framework::OpKernel<T> {
       for_range(matrix_band_part_functor);
     }
 
-    // TODO(guosheng): Add callback to check info
     auto info = memory::Alloc(dev_ctx, sizeof(int) * batch_count);
     auto* info_ptr = reinterpret_cast<int*>(info->ptr());
 
@@ -96,6 +95,20 @@ class CholeskyGPUKernel : public framework::OpKernel<T> {
 #if CUDA_VERSION >= 9020 && !defined(_WIN32)
     }
 #endif
+    // check the info
+    std::vector<int> error_info;  // only for checking positive matrix
+    error_info.resize(batch_count);
+
+    memory::Copy(platform::CPUPlace(), error_info.data(),
+                 BOOST_GET_CONST(platform::CUDAPlace, dev_ctx.GetPlace()),
+                 info_ptr, sizeof(int) * batch_count, dev_ctx.stream());
+
+    for (int i = 0; i < batch_count; ++i) {
+      PADDLE_ENFORCE_EQ(error_info[i], 0,
+                        platform::errors::PreconditionNotMet(
+                            "For batch [%d]: U(%d, %d) is zero, singular U.", i,
+                            error_info[i], error_info[i]));
+    }
   }
 
   void Potrf(const platform::CUDADeviceContext& dev_ctx, cublasFillMode_t uplo,
diff --git a/paddle/fluid/operators/cholesky_op.h b/paddle/fluid/operators/cholesky_op.h
index b0280b00ecf447d36b199e6b6765fa7928e081f0..15dd8315362ed0221c5c8b9c523af37da38dfd7e 100644
--- a/paddle/fluid/operators/cholesky_op.h
+++ b/paddle/fluid/operators/cholesky_op.h
@@ -59,22 +59,24 @@ class CholeskyCPUKernel : public framework::OpKernel<T> {
             Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>,
             Eigen::UpLoType::Upper>
             llt_decomposition(input);
-        PADDLE_ENFORCE_EQ(
-            llt_decomposition.info(), Eigen::Success,
-            platform::errors::InvalidArgument(
-                "Cholesky decomposition was not successful. The input matrice "
-                "might not be not be positive definite."));
+        PADDLE_ENFORCE_EQ(llt_decomposition.info(), Eigen::Success,
+                          platform::errors::InvalidArgument(
+                              "Cholesky decomposition was not successful. The "
+                              "%d-th input matrice "
+                              "might not be not be positive definite.",
+                              i));
         output = llt_decomposition.matrixU();
       } else {
         Eigen::LLT<
             Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>,
             Eigen::UpLoType::Lower>
             llt_decomposition(input);
-        PADDLE_ENFORCE_EQ(
-            llt_decomposition.info(), Eigen::Success,
-            platform::errors::InvalidArgument(
-                "Cholesky decomposition was not successful. The input matrice "
-                "might not be not be positive definite."));
+        PADDLE_ENFORCE_EQ(llt_decomposition.info(), Eigen::Success,
+                          platform::errors::InvalidArgument(
+                              "Cholesky decomposition was not successful. The "
+                              "%d-th input matrice "
+                              "might not be not be positive definite.",
+                              i));
         output = llt_decomposition.matrixL();
       }
     }
diff --git a/python/paddle/fluid/tests/unittests/test_cholesky_op.py b/python/paddle/fluid/tests/unittests/test_cholesky_op.py
index f3e6c079eedc8effc948a44e08a5dcdcae8d3081..ab08a0aacbf08768ffff43974ee9a7c7dd4a7288 100644
--- a/python/paddle/fluid/tests/unittests/test_cholesky_op.py
+++ b/python/paddle/fluid/tests/unittests/test_cholesky_op.py
@@ -100,5 +100,45 @@ class TestDygraph(unittest.TestCase):
         out = paddle.cholesky(x, upper=False)
 
 
+class TestCholeskySingularAPI(unittest.TestCase):
+    def setUp(self):
+        self.places = [fluid.CPUPlace()]
+        if core.is_compiled_with_cuda():
+            self.places.append(fluid.CUDAPlace(0))
+
+    def check_static_result(self, place, with_out=False):
+        with fluid.program_guard(fluid.Program(), fluid.Program()):
+            input = fluid.data(name="input", shape=[4, 4], dtype="float64")
+            result = paddle.cholesky(input)
+
+            input_np = np.zeros([4, 4]).astype("float64")
+
+            exe = fluid.Executor(place)
+            try:
+                fetches = exe.run(fluid.default_main_program(),
+                                  feed={"input": input_np},
+                                  fetch_list=[result])
+            except fluid.core.EnforceNotMet as ex:
+                print("The mat is singular")
+                pass
+
+    def test_static(self):
+        for place in self.places:
+            self.check_static_result(place=place)
+
+    def test_dygraph(self):
+        for place in self.places:
+            with fluid.dygraph.guard(place):
+                input_np = np.array([[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
+                                     [[10, 11, 12], [13, 14, 15],
+                                      [16, 17, 18]]]).astype("float64")
+                input = fluid.dygraph.to_variable(input_np)
+                try:
+                    result = paddle.cholesky(input)
+                except fluid.core.EnforceNotMet as ex:
+                    print("The mat is singular")
+                    pass
+
+
 if __name__ == "__main__":
     unittest.main()