diff --git a/pandas/tests/groupby/test_apply.py b/pandas/tests/groupby/test_apply.py
index db5c4af9c6f53..176efdb6204da 100644
--- a/pandas/tests/groupby/test_apply.py
+++ b/pandas/tests/groupby/test_apply.py
@@ -681,6 +681,23 @@ def test_apply_aggregating_timedelta_and_datetime():
     tm.assert_frame_equal(result, expected)
 
 
+def test_apply_groupby_datetimeindex():
+    # GH 26182
+    # groupby apply failed on dataframe with DatetimeIndex
+
+    data = [["A", 10], ["B", 20], ["B", 30], ["C", 40], ["C", 50]]
+    df = pd.DataFrame(
+        data, columns=["Name", "Value"], index=pd.date_range("2020-09-01", "2020-09-05")
+    )
+
+    result = df.groupby("Name").sum()
+
+    expected = pd.DataFrame({"Name": ["A", "B", "C"], "Value": [10, 50, 90]})
+    expected.set_index("Name", inplace=True)
+
+    tm.assert_frame_equal(result, expected)
+
+
 def test_time_field_bug():
     # Test a fix for the following error related to GH issue 11324 When
     # non-key fields in a group-by dataframe contained time-based fields