diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 1ac6d075946dd..37c7e9267b39a 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -536,11 +536,11 @@ Groupby/Resample/Rolling
 
 - Bug in :func:`pandas.core.groupby.GroupBy.first` and :func:`pandas.core.groupby.GroupBy.last` with ``as_index=False`` leading to the loss of timezone information (:issue:`15884`)
 - Bug in :meth:`DatetimeIndex.resample` when downsampling across a DST boundary (:issue:`8531`)
--
--
-
+- Bug where ``ValueError`` is wrongly raised when calling :func:`~pandas.core.groupby.SeriesGroupBy.count` method of a
+  ``SeriesGroupBy`` when the grouping variable only contains NaNs and numpy version < 1.13 (:issue:`21956`).
 - Multiple bugs in :func:`pandas.core.Rolling.min` with ``closed='left'` and a
   datetime-like index leading to incorrect results and also segfault. (:issue:`21704`)
+-
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index fdededc325b03..4c87f6122b956 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -1207,7 +1207,7 @@ def count(self):
 
         mask = (ids != -1) & ~isna(val)
         ids = ensure_platform_int(ids)
-        out = np.bincount(ids[mask], minlength=ngroups or 0)
+        out = np.bincount(ids[mask], minlength=ngroups or None)
 
         return Series(out,
                       index=self.grouper.result_index,
diff --git a/pandas/tests/groupby/test_counting.py b/pandas/tests/groupby/test_counting.py
index 787d99086873e..a14b6ff014f37 100644
--- a/pandas/tests/groupby/test_counting.py
+++ b/pandas/tests/groupby/test_counting.py
@@ -212,3 +212,13 @@ def test_count_with_datetimelike(self, datetimelike):
         expected = DataFrame({'y': [2, 1]}, index=['a', 'b'])
         expected.index.name = "x"
         assert_frame_equal(expected, res)
+
+    def test_count_with_only_nans_in_first_group(self):
+        # GH21956
+        df = DataFrame({'A': [np.nan, np.nan], 'B': ['a', 'b'], 'C': [1, 2]})
+        result = df.groupby(['A', 'B']).C.count()
+        mi = MultiIndex(levels=[[], ['a', 'b']],
+                        labels=[[], []],
+                        names=['A', 'B'])
+        expected = Series([], index=mi, dtype=np.int64, name='C')
+        assert_series_equal(result, expected, check_index_type=False)