diff --git a/python/paddle/fluid/tests/unittests/test_linalg_lstsq_op.py b/python/paddle/fluid/tests/unittests/test_linalg_lstsq_op.py
index 82576ab1bd1bf7dd0c5ac9deefebda4b028eab20..94dc901a56d0c92d47dd95f4fe1029e4919a2571 100644
--- a/python/paddle/fluid/tests/unittests/test_linalg_lstsq_op.py
+++ b/python/paddle/fluid/tests/unittests/test_linalg_lstsq_op.py
@@ -278,5 +278,38 @@ class LinalgLstsqTestCaseLarge2(LinalgLstsqTestCase):
         self._input_shape_2 = (50, 300)
 
 
+class TestLinalgLstsqAPIError(unittest.TestCase):
+    def setUp(self):
+        pass
+
+    def test_api_errors(self):
+        def test_x_bad_shape():
+            x = paddle.to_tensor(np.random.random(size=(5)), dtype=np.float32)
+            y = paddle.to_tensor(
+                np.random.random(size=(5, 15)), dtype=np.float32
+            )
+            out = paddle.linalg.lstsq(x, y, driver='gelsy')
+
+        def test_y_bad_shape():
+            x = paddle.to_tensor(
+                np.random.random(size=(5, 10)), dtype=np.float32
+            )
+            y = paddle.to_tensor(np.random.random(size=(5)), dtype=np.float32)
+            out = paddle.linalg.lstsq(x, y, driver='gelsy')
+
+        def test_shape_dismatch():
+            x = paddle.to_tensor(
+                np.random.random(size=(5, 10)), dtype=np.float32
+            )
+            y = paddle.to_tensor(
+                np.random.random(size=(4, 15)), dtype=np.float32
+            )
+            out = paddle.linalg.lstsq(x, y, driver='gelsy')
+
+        self.assertRaises(ValueError, test_x_bad_shape)
+        self.assertRaises(ValueError, test_y_bad_shape)
+        self.assertRaises(ValueError, test_shape_dismatch)
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/python/paddle/tensor/linalg.py b/python/paddle/tensor/linalg.py
index 4cce1b01968a196250d9346ec4a4e173e21f6892..46f11130c035449480d05564c8055dc5c9d4b340 100644
--- a/python/paddle/tensor/linalg.py
+++ b/python/paddle/tensor/linalg.py
@@ -3171,13 +3171,26 @@ def lstsq(x, y, rcond=None, driver=None, name=None):
     else:
         raise RuntimeError("Only support lstsq api for CPU or CUDA device.")
 
-    if x.dtype == y.dtype and x.dtype in (paddle.float32, paddle.float64):
-        pass
-    else:
+    if not (x.dtype == y.dtype and x.dtype in (paddle.float32, paddle.float64)):
         raise ValueError(
             "Only support x and y have the same dtype such as 'float32' and 'float64'."
         )
 
+    if x.ndim < 2:
+        raise ValueError(
+            f"The shape of x should be (*, M, N), but received ndim is [{x.ndim} < 2]"
+        )
+
+    if y.ndim < 2:
+        raise ValueError(
+            f"The shape of y should be (*, M, K), but received ndim is [{y.ndim} < 2]"
+        )
+
+    if x.shape[-2] != y.shape[-2]:
+        raise ValueError(
+            f"x with shape (*, M = {x.shape[-2]}, N) and y with shape (*, M = {y.shape[-2]}, K) should have same M."
+        )
+
     if rcond is None:
         if x.dtype == paddle.float32:
             rcond = 1e-7 * max(x.shape[-2], x.shape[-1])