diff --git a/paddle/fluid/eager/auto_code_generator/generator/eager_gen.py b/paddle/fluid/eager/auto_code_generator/generator/eager_gen.py
index 70003b48cc897..1bc700d5f53ec 100644
--- a/paddle/fluid/eager/auto_code_generator/generator/eager_gen.py
+++ b/paddle/fluid/eager/auto_code_generator/generator/eager_gen.py
@@ -73,6 +73,7 @@
     "add_triple_grad",
     "silu_double_grad",
     "tanh_triple_grad",
+    "minimum_double_grad",
 ]
 
 # white ops list whose kernel can automaically do type promotion.
diff --git a/paddle/fluid/prim/api/composite_backward/composite_double_backward_api.h b/paddle/fluid/prim/api/composite_backward/composite_double_backward_api.h
index abafca001a354..4e9f09a0c52f3 100644
--- a/paddle/fluid/prim/api/composite_backward/composite_double_backward_api.h
+++ b/paddle/fluid/prim/api/composite_backward/composite_double_backward_api.h
@@ -89,6 +89,32 @@ void cos_double_grad(const Tensor& x,
   }
 }
 
+template <typename T>
+void minimum_double_grad(const Tensor& x,
+                         const Tensor& y,
+                         const paddle::optional<Tensor>& grad_x_grad,
+                         const paddle::optional<Tensor>& grad_y_grad,
+                         Tensor* grad_out_grad) {
+  if (grad_out_grad) {
+    if (grad_x_grad && grad_y_grad) {
+      auto x_mask = cast<T>(less_than<T>(x, y), grad_x_grad.get().dtype());
+      auto ddout =
+          grad_x_grad.get() * x_mask + grad_y_grad.get() * (1 - x_mask);
+      set_output<T>(ddout, grad_out_grad);
+    } else if (grad_x_grad) {
+      auto x_mask = cast<T>(less_than<T>(x, y), grad_x_grad.get().dtype());
+      auto ddout = grad_x_grad.get() * x_mask;
+      set_output<T>(ddout, grad_out_grad);
+    } else if (grad_y_grad) {
+      auto y_mask = cast<T>(greater_equal<T>(x, y), grad_y_grad.get().dtype());
+      auto ddout = grad_y_grad.get() * y_mask;
+      set_output<T>(ddout, grad_out_grad);
+    } else {
+      grad_out_grad = nullptr;
+    }
+  }
+}
+
 template <typename T>
 void tanh_triple_grad(const Tensor& out,
                       const Tensor& grad_out_forward,
diff --git a/paddle/phi/api/yaml/legacy_backward.yaml b/paddle/phi/api/yaml/legacy_backward.yaml
index e5529aa6c5efa..2ca26f1efbdd5 100755
--- a/paddle/phi/api/yaml/legacy_backward.yaml
+++ b/paddle/phi/api/yaml/legacy_backward.yaml
@@ -421,6 +421,7 @@
   kernel :
     func : minimum_grad
   composite : minimum_grad(x, y, out_grad, axis, x_grad, y_grad)
+  backward : minimum_double_grad
 
 - backward_op : mish_grad
   forward : mish (Tensor x, float lambda) -> Tensor(out)
@@ -876,6 +877,13 @@
     func : fused_gemm_epilogue_grad
   optional : reserve_space
 
+- backward_op: minimum_double_grad
+  forward: minimum_grad(Tensor x, Tensor y, Tensor grad_out) -> Tensor(grad_x), Tensor(grad_y)
+  args: (Tensor x, Tensor y, Tensor grad_x_grad, Tensor grad_y_grad)
+  output: Tensor(grad_out_grad)
+  composite: minimum_double_grad(x, y, grad_x_grad, grad_y_grad, grad_out_grad)
+  optional : grad_x_grad, grad_y_grad
+
 - backward_op: unpool_grad
   forward: unpool (Tensor x, Tensor indices, int[] ksize, int[] strides, int[] padding,  IntArray output_size, str data_format) -> Tensor(out)
   args: (Tensor x, Tensor indices, Tensor out, Tensor out_grad, int[] ksize, int[] strides, int[] padding, IntArray output_size, str data_format)
diff --git a/test/prim/prim/vjp/test_comp_high_grad.py b/test/prim/prim/vjp/test_comp_high_grad.py
index 96762679df519..204999c9ff05c 100644
--- a/test/prim/prim/vjp/test_comp_high_grad.py
+++ b/test/prim/prim/vjp/test_comp_high_grad.py
@@ -411,5 +411,79 @@ def test_high_grad(self):
             self.func_triple(p)
 
 
+@param.parameterized_class(
+    ('shape1', 'shape2'),
+    [
+        (
+            [2, 3, 4],
+            [2, 3, 4],
+        ),
+        (
+            [2, 3, 3, 4],
+            [3, 1, 4],
+        ),
+        (
+            [2, 3, 3, 4],
+            [3, 1, 1],
+        ),
+        (
+            [2, 3, 3, 4],
+            [2, 3, 1, 4],
+        ),
+        (
+            [2, 3, 3, 4],
+            [2, 3, 1, 1],
+        ),
+    ],
+)
+class TestMinimumHighGradCheck(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.shape1 = cls.shape1
+        cls.shape2 = cls.shape2
+
+    def minimum_wrapper(self, x):
+        return paddle.minimum(x[0], x[1])
+
+    @prog_scope()
+    def func_double(self, place):
+        shape1 = self.shape1
+        shape2 = self.shape2
+        eps = 0.0005
+        dtype = np.float64
+        x = paddle.static.data('x', shape1, dtype=dtype)
+        y = paddle.static.data('y', shape2, dtype=dtype)
+        x.persistable = True
+        y.persistable = True
+        out = paddle.minimum(x, y)
+        x_arr = np.random.uniform(-1, 1, shape1).astype(dtype)
+        y_arr = np.random.uniform(-2, 2, shape2).astype(dtype)
+        x_arr[np.abs(x_arr) < 0.005] = 0.002
+        y_arr[np.abs(y_arr) < 0.005] = 0.002
+        from paddle.base import core
+
+        core._set_prim_backward_enabled(True)
+        core._set_prim_backward_blacklist("minimum_grad")
+        gradient_checker.double_grad_check(
+            [x, y], y=out, x_init=[x_arr, y_arr], place=place, eps=eps
+        )
+        gradient_checker.double_grad_check_for_dygraph(
+            self.minimum_wrapper,
+            [x, y],
+            y=out,
+            x_init=[x_arr, y_arr],
+            place=place,
+        )
+        core._set_prim_backward_enabled(False)
+
+    def test_high_grad(self):
+        paddle.enable_static()
+        places = [base.CPUPlace()]
+        if core.is_compiled_with_cuda():
+            places.append(base.CUDAPlace(0))
+        for p in places:
+            self.func_double(p)
+
+
 if __name__ == '__main__':
     unittest.main()