diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index 5384b228850f4..b4a243671e287 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -2846,3 +2846,22 @@ def test_sum_of_booleans(n):
     result = df.groupby("groupby_col").sum()
     expected = DataFrame({"bool": [n]}, index=Index([1], name="groupby_col"))
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("method", ["head", "tail", "nth", "first", "last"])
+def test_groupby_method_drop_na(method):
+    # GH 21755
+    df = DataFrame({"A": ["a", np.nan, "b", np.nan, "c"], "B": range(5)})
+
+    if method == "nth":
+        result = getattr(df.groupby("A"), method)(n=0)
+    else:
+        result = getattr(df.groupby("A"), method)()
+
+    if method in ["first", "last"]:
+        expected = DataFrame({"B": [0, 2, 4]}).set_index(
+            Series(["a", "b", "c"], name="A")
+        )
+    else:
+        expected = DataFrame({"A": ["a", "b", "c"], "B": [0, 2, 4]}, index=[0, 2, 4])
+    tm.assert_frame_equal(result, expected)