diff --git a/paddle/phi/infermeta/unary.cc b/paddle/phi/infermeta/unary.cc
index 998001a008ebeb5c2d98503c6e0c91da562ad252..a8ea3ad760330581f58c14c767544e2cd7eef9a2 100644
--- a/paddle/phi/infermeta/unary.cc
+++ b/paddle/phi/infermeta/unary.cc
@@ -220,18 +220,26 @@ void ArgsortInferMeta(const MetaTensor& input,
                       MetaTensor* indices) {
   auto in_dims = input.dims();
   auto num_dims = in_dims.size();
-  PADDLE_ENFORCE_GE(
-      axis,
-      -num_dims,
-      phi::errors::InvalidArgument("'axis'(%d) must be greater than or equal to"
-                                   " -num_dims(%d).",
-                                   axis,
-                                   -num_dims));
-  PADDLE_ENFORCE_LT(
-      axis,
-      num_dims,
-      phi::errors::InvalidArgument(
-          "'axis'(%d) must be less than num_dims(%d).", axis, num_dims));
+  if (num_dims > 0) {
+    PADDLE_ENFORCE_GE(axis,
+                      -num_dims,
+                      phi::errors::InvalidArgument(
+                          "'axis'(%d) must be greater than or equal to"
+                          " -num_dims(%d).",
+                          axis,
+                          -num_dims));
+    PADDLE_ENFORCE_LT(
+        axis,
+        num_dims,
+        phi::errors::InvalidArgument(
+            "'axis'(%d) must be less than num_dims(%d).", axis, num_dims));
+  } else {  // 0-dim tensor
+    PADDLE_ENFORCE_EQ(
+        axis == 0 || axis == -1,
+        1,
+        phi::errors::InvalidArgument(
+            "'axis'(%d) must be 0 or -1 if input tensor is 0-dim.", axis));
+  }
 
   output->share_dims(input);
   output->set_dtype(input.dtype());
diff --git a/paddle/phi/kernels/cpu/argsort_grad_kernel.cc b/paddle/phi/kernels/cpu/argsort_grad_kernel.cc
index 1e60847232c70b2af9382331809d73a7208fc956..81616dafc0a8be8409adfa224f793187fe723ceb 100644
--- a/paddle/phi/kernels/cpu/argsort_grad_kernel.cc
+++ b/paddle/phi/kernels/cpu/argsort_grad_kernel.cc
@@ -58,6 +58,7 @@ void ArgsortGradKernel(const Context& dev_ctx,
                        bool descending,
                        DenseTensor* in_grad) {
   auto in_dims = indices.dims();
+  auto rank = input.dims().size();
   axis = (axis < 0) ? (in_dims.size() + axis) : axis;
   dev_ctx.template Alloc<T>(in_grad);
   auto dxt = EigenVector<T>::Flatten(*in_grad);
@@ -65,6 +66,11 @@ void ArgsortGradKernel(const Context& dev_ctx,
   dxt.device(place) = dxt.constant(static_cast<T>(0));
   if (out_grad.numel() == 0) return;
 
+  if (rank == 0) {
+    phi::Copy<Context>(dev_ctx, out_grad, dev_ctx.GetPlace(), false, in_grad);
+    return;
+  }
+
   // Do full assign
   if (axis == -1 || axis + 1 == in_dims.size()) {
     const int64_t input_height =
diff --git a/paddle/phi/kernels/cpu/argsort_kernel.cc b/paddle/phi/kernels/cpu/argsort_kernel.cc
index 8621a717e1018f8a6e9a73b6e7440a1331cc63bd..97f8fb67ed1d6462b27c7d3250dca9fc10266e1c 100644
--- a/paddle/phi/kernels/cpu/argsort_kernel.cc
+++ b/paddle/phi/kernels/cpu/argsort_kernel.cc
@@ -18,6 +18,7 @@
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/funcs/eigen/common.h"
 #include "paddle/phi/kernels/funcs/eigen/eigen_function.h"
+#include "paddle/phi/kernels/funcs/math_function.h"
 #include "paddle/phi/kernels/transpose_kernel.h"
 
 namespace phi {
@@ -75,9 +76,18 @@ void ArgsortKernel(const Context& dev_ctx,
                    DenseTensor* output,
                    DenseTensor* indices) {
   auto in_dims = input.dims();
+  auto rank = in_dims.size();
   axis = (axis < 0) ? (in_dims.size() + axis) : axis;
   T* out_data = dev_ctx.template Alloc<T>(output);
 
+  // For 0D Tensor
+  if (rank == 0) {
+    phi::Copy<Context>(dev_ctx, input, dev_ctx.GetPlace(), false, output);
+    dev_ctx.template Alloc<int64_t>(indices);
+    phi::funcs::set_constant(dev_ctx, indices, 0);
+    return;
+  }
+
   // Do full sort
   if (axis == -1 || axis + 1 == in_dims.size()) {
     const int64_t input_height =
diff --git a/paddle/phi/kernels/gpu/argsort_grad_kernel.cu b/paddle/phi/kernels/gpu/argsort_grad_kernel.cu
index a2d149cb2e438325381fe6ae68d04e52ff4f75ee..b8d9df64c23efb54fcc81a3ff43fb26051edd850 100644
--- a/paddle/phi/kernels/gpu/argsort_grad_kernel.cu
+++ b/paddle/phi/kernels/gpu/argsort_grad_kernel.cu
@@ -28,6 +28,7 @@ namespace cub = hipcub;
 
 #include "paddle/phi/backends/gpu/gpu_context.h"
 #include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/funcs/math_function.h"
 #include "paddle/phi/kernels/primitive/functor_primitives.h"
 #include "paddle/phi/kernels/transpose_kernel.h"
 
@@ -141,11 +142,18 @@ void ArgsortGradKernel(const Context& dev_ctx,
                        bool descending,
                        DenseTensor* in_grad) {
   dev_ctx.template Alloc<T>(in_grad);
+  phi::funcs::set_constant(dev_ctx, in_grad, 0.0);
   if (out_grad.numel() == 0) return;
   auto in_dims = in_grad->dims();
+  auto rank = in_dims.size();
   axis = (axis < 0) ? (in_dims.size() + axis) : axis;
   int64_t size = in_grad->numel();
 
+  if (rank == 0) {
+    phi::Copy<Context>(dev_ctx, out_grad, dev_ctx.GetPlace(), false, in_grad);
+    return;
+  }
+
   // Parallel acceleration when the input size is equal to the length of the
   // ‘axis’ dimension.
   // Compared to 'special case for full sort' below, the gradient calculation
diff --git a/paddle/phi/kernels/gpu/argsort_kernel.cu b/paddle/phi/kernels/gpu/argsort_kernel.cu
index 1c3825b90e2101b6465abbdc66c4211af00c9989..13455a7639cdb6ab112151aa0e380fd26bc08f66 100644
--- a/paddle/phi/kernels/gpu/argsort_kernel.cu
+++ b/paddle/phi/kernels/gpu/argsort_kernel.cu
@@ -30,6 +30,7 @@ namespace cub = hipcub;
 #include "paddle/phi/backends/gpu/gpu_info.h"
 #include "paddle/phi/core/kernel_registry.h"
 #include "paddle/phi/kernels/funcs/blas/blas.h"
+#include "paddle/phi/kernels/funcs/math_function.h"
 #include "paddle/phi/kernels/primitive/functor_primitives.h"
 #include "paddle/phi/kernels/transpose_kernel.h"
 
@@ -396,6 +397,7 @@ void ArgsortKernel(const Context &dev_ctx,
                    DenseTensor *output,
                    DenseTensor *indices) {
   auto in_dims = input.dims();
+  auto rank = in_dims.size();
   axis = (axis < 0) ? (in_dims.size() + axis) : axis;
 
   const T *in_data = input.data<T>();
@@ -403,6 +405,12 @@ void ArgsortKernel(const Context &dev_ctx,
   T *out_data = dev_ctx.template Alloc<T>(output);
   int64_t *ids_data = dev_ctx.template Alloc<int64_t>(indices);
 
+  if (rank == 0) {
+    phi::Copy<Context>(dev_ctx, input, dev_ctx.GetPlace(), false, output);
+    phi::funcs::set_constant(dev_ctx, indices, 0);
+    return;
+  }
+
   // Use thrust for parallel acceleration when the input size is equal to the
   // length of the ‘axis’ dimension.
   // Compared to the following 'Special case for full sort', ascending sort is
diff --git a/paddle/phi/kernels/xpu/argsort_grad_kernel.cc b/paddle/phi/kernels/xpu/argsort_grad_kernel.cc
index 371cc7d39c2900c55f12d1508a2e277fa4b5db7f..4ebab7b37fc301a655480d1fd2c600028b3d1a86 100644
--- a/paddle/phi/kernels/xpu/argsort_grad_kernel.cc
+++ b/paddle/phi/kernels/xpu/argsort_grad_kernel.cc
@@ -29,6 +29,7 @@ void ArgsortGradKernel(const Context& dev_ctx,
                        bool descending,
                        DenseTensor* in_grad) {
   auto in_dims = indices.dims();
+  auto rank = in_dims.size();
   axis = (axis < 0) ? (in_dims.size() + axis) : axis;
   dev_ctx.template Alloc<T>(in_grad);
 
@@ -40,6 +41,11 @@ void ArgsortGradKernel(const Context& dev_ctx,
 
   if (out_grad.numel() == 0) return;
 
+  if (rank == 0) {
+    phi::Copy<Context>(dev_ctx, out_grad, dev_ctx.GetPlace(), false, in_grad);
+    return;
+  }
+
   bool is_need_transpose = true;
   if (axis == -1 || axis + 1 == in_dims.size()) {
     is_need_transpose = false;
diff --git a/paddle/phi/kernels/xpu/argsort_kernel.cc b/paddle/phi/kernels/xpu/argsort_kernel.cc
index 0a71ec71463d4173f29dfd0bde7e9255e465f71e..4fdb42f69fd87779418abf4fc9ef23169392704e 100644
--- a/paddle/phi/kernels/xpu/argsort_kernel.cc
+++ b/paddle/phi/kernels/xpu/argsort_kernel.cc
@@ -17,6 +17,7 @@
 #include "paddle/phi/backends/xpu/enforce_xpu.h"
 #include "paddle/phi/backends/xpu/xpu_context.h"
 #include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/funcs/math_function.h"
 
 namespace phi {
 
@@ -171,6 +172,7 @@ void ArgsortKernel(const Context& dev_ctx,
                    DenseTensor* output,
                    DenseTensor* indices) {
   auto in_dims = input.dims();
+  auto rank = in_dims.size();
   axis = (axis < 0) ? (in_dims.size() + axis) : axis;
   int n = in_dims[axis];
 
@@ -178,6 +180,12 @@ void ArgsortKernel(const Context& dev_ctx,
   auto output_data = dev_ctx.template Alloc<T>(output);
   auto indices_data = dev_ctx.template Alloc<int64_t>(indices);
 
+  if (rank == 0) {
+    phi::Copy<Context>(dev_ctx, input, dev_ctx.GetPlace(), false, output);
+    phi::funcs::set_constant(dev_ctx, indices, 0);
+    return;
+  }
+
   int len_before = phi::product(phi::slice_ddim(in_dims, 0, axis));
   int len_after =
       phi::product(phi::slice_ddim(in_dims, axis + 1, in_dims.size()));
diff --git a/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py b/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py
index 8523fb44b982fe60140efc7e8ef25c15d891126a..546c0c48f9b585c6b3a1549a9288fe386a1392d2 100644
--- a/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py
+++ b/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py
@@ -855,6 +855,50 @@ class TestSundryAPI(unittest.TestCase):
         self.assertEqual(out.shape, [])
         self.assertEqual(out.grad.shape, [])
 
+    def test_sort(self):
+        x1 = paddle.rand([])
+        x2 = paddle.rand([])
+        x1.stop_gradient = False
+        x2.stop_gradient = False
+        out1 = paddle.sort(x1, axis=-1)
+        out2 = paddle.sort(x2, axis=0)
+
+        out1.backward()
+        out2.backward()
+
+        self.assertEqual(out1.shape, [])
+        self.assertEqual(out2.shape, [])
+        self.assertEqual(out1.numpy(), x1.numpy())
+        self.assertEqual(out2.numpy(), x2.numpy())
+        self.assertEqual(out1.grad.shape, [])
+        self.assertEqual(out2.grad.shape, [])
+        self.assertEqual(x1.grad.shape, [])
+        self.assertEqual(x2.grad.shape, [])
+        self.assertEqual(x1.grad.numpy(), 1)
+        self.assertEqual(x2.grad.numpy(), 1)
+
+    def test_argsort(self):
+        x1 = paddle.rand([])
+        x2 = paddle.rand([])
+        x1.stop_gradient = False
+        x2.stop_gradient = False
+        out1 = paddle.argsort(x1, axis=-1)
+        out2 = paddle.argsort(x2, axis=0)
+
+        out1.backward()
+        out2.backward()
+
+        self.assertEqual(out1.shape, [])
+        self.assertEqual(out2.shape, [])
+        self.assertEqual(out1.numpy(), 0)
+        self.assertEqual(out2.numpy(), 0)
+        self.assertEqual(out1.grad.shape, [])
+        self.assertEqual(out2.grad.shape, [])
+        self.assertEqual(x1.grad.shape, [])
+        self.assertEqual(x2.grad.shape, [])
+        self.assertEqual(x1.grad.numpy(), 0)
+        self.assertEqual(x2.grad.numpy(), 0)
+
 
 class TestSundryAPIStatic(unittest.TestCase):
     def setUp(self):
@@ -1182,6 +1226,42 @@ class TestSundryAPIStatic(unittest.TestCase):
         self.assertEqual(res1.shape, ())
         self.assertEqual(res2.shape, ())
 
+    @prog_scope()
+    def test_sort(self):
+        x1 = paddle.rand([])
+        x1.stop_gradient = False
+        out1 = paddle.sort(x1, axis=-1)
+        paddle.static.append_backward(out1)
+
+        x2 = paddle.rand([])
+        x2.stop_gradient = False
+        out2 = paddle.sort(x2, axis=0)
+        paddle.static.append_backward(out2)
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out1, out2])
+
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, ())
+
+    @prog_scope()
+    def test_argsort(self):
+        x1 = paddle.rand([])
+        x1.stop_gradient = False
+        out1 = paddle.argsort(x1, axis=-1)
+        paddle.static.append_backward(out1)
+
+        x2 = paddle.rand([])
+        x2.stop_gradient = False
+        out2 = paddle.argsort(x2, axis=0)
+        paddle.static.append_backward(out2)
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out1, out2])
+
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, ())
+
 
 # Use to test API whose zero-dim input tensors don't have grad and not need to test backward in OpTest.
 class TestNoBackwardAPI(unittest.TestCase):
diff --git a/python/paddle/fluid/tests/unittests/xpu/test_zero_dim_tensor_xpu.py b/python/paddle/fluid/tests/unittests/xpu/test_zero_dim_tensor_xpu.py
index 8ceee04c206b10c31f863447c528bc978f9ceb1e..c0e0de0ac13358ab312e6398351223e583d0a6c1 100644
--- a/python/paddle/fluid/tests/unittests/xpu/test_zero_dim_tensor_xpu.py
+++ b/python/paddle/fluid/tests/unittests/xpu/test_zero_dim_tensor_xpu.py
@@ -646,6 +646,50 @@ class TestSundryAPI(unittest.TestCase):
         out = paddle.reshape_(x, new_shape)
         self.assertEqual(out.shape, [1, 1])
 
+    def test_sort(self):
+        x1 = paddle.rand([])
+        x2 = paddle.rand([])
+        x1.stop_gradient = False
+        x2.stop_gradient = False
+        out1 = paddle.sort(x1, axis=-1)
+        out2 = paddle.sort(x2, axis=0)
+
+        out1.backward()
+        out2.backward()
+
+        self.assertEqual(out1.shape, [])
+        self.assertEqual(out2.shape, [])
+        self.assertEqual(out1.numpy(), x1.numpy())
+        self.assertEqual(out2.numpy(), x2.numpy())
+        self.assertEqual(out1.grad.shape, [])
+        self.assertEqual(out2.grad.shape, [])
+        self.assertEqual(x1.grad.shape, [])
+        self.assertEqual(x2.grad.shape, [])
+        self.assertEqual(x1.grad.numpy(), 1)
+        self.assertEqual(x2.grad.numpy(), 1)
+
+    def test_argsort(self):
+        x1 = paddle.rand([])
+        x2 = paddle.rand([])
+        x1.stop_gradient = False
+        x2.stop_gradient = False
+        out1 = paddle.argsort(x1, axis=-1)
+        out2 = paddle.argsort(x2, axis=0)
+
+        out1.backward()
+        out2.backward()
+
+        self.assertEqual(out1.shape, [])
+        self.assertEqual(out2.shape, [])
+        self.assertEqual(out1.numpy(), 0)
+        self.assertEqual(out2.numpy(), 0)
+        self.assertEqual(out1.grad.shape, [])
+        self.assertEqual(out2.grad.shape, [])
+        self.assertEqual(x1.grad.shape, [])
+        self.assertEqual(x2.grad.shape, [])
+        self.assertEqual(x1.grad.numpy(), 0)
+        self.assertEqual(x2.grad.numpy(), 0)
+
 
 # Use to test API whose zero-dim input tensors don't have grad and not need to test backward in OpTest.
 class TestNoBackwardAPI(unittest.TestCase):