diff --git a/pandas/tests/apply/test_frame_apply.py b/pandas/tests/apply/test_frame_apply.py
index c7eb8c0332e84..f0f8b3befadcb 100644
--- a/pandas/tests/apply/test_frame_apply.py
+++ b/pandas/tests/apply/test_frame_apply.py
@@ -1665,3 +1665,15 @@ def foo2(x, b=2, c=0):
         columns=MultiIndex.from_tuples([("x", "foo1"), ("x", "foo2")]),
     )
     tm.assert_frame_equal(result, expected)
+
+
+def test_agg_std():
+    df = DataFrame(np.arange(6).reshape(3, 2), columns=["A", "B"])
+
+    result = df.agg(np.std)
+    expected = Series({"A": 2.0, "B": 2.0}, dtype=float)
+    tm.assert_series_equal(result, expected)
+
+    result = df.agg([np.std])
+    expected = DataFrame({"A": 2.0, "B": 2.0}, index=["std"])
+    tm.assert_frame_equal(result, expected)