diff --git a/pandas/tests/groupby/test_categorical.py b/pandas/tests/groupby/test_categorical.py
index a33e4efbe3b6d..0e72899818139 100644
--- a/pandas/tests/groupby/test_categorical.py
+++ b/pandas/tests/groupby/test_categorical.py
@@ -1794,3 +1794,21 @@ def test_groupby_categorical_observed_nunique():
         name="c",
     )
     tm.assert_series_equal(result, expected)
+
+
+def test_groupby_categorical_aggregate_functions():
+    # GH#37275
+    dtype = pd.CategoricalDtype(categories=["small", "big"], ordered=True)
+    df = DataFrame(
+        [[1, "small"], [1, "big"], [2, "small"]], columns=["grp", "description"]
+    ).astype({"description": dtype})
+
+    result = df.groupby("grp")["description"].max()
+    expected = Series(
+        ["big", "small"],
+        index=Index([1, 2], name="grp"),
+        name="description",
+        dtype=pd.CategoricalDtype(categories=["small", "big"], ordered=True),
+    )
+
+    tm.assert_series_equal(result, expected)