diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index ae4d5ea692066..0ab95dd260a9c 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -442,6 +442,7 @@ Groupby/resample/rolling
 - Bug in :meth:`Rolling.sum()` returned wrong values when dtypes where mixed between float and integer and axis was equal to one (:issue:`20649`, :issue:`35596`)
 - Bug in :meth:`Rolling.count` returned ``np.nan`` with :class:`pandas.api.indexers.FixedForwardWindowIndexer` as window, ``min_periods=0`` and only missing values in window (:issue:`35579`)
 - Bug where :class:`pandas.core.window.Rolling` produces incorrect window sizes when using a ``PeriodIndex`` (:issue:`34225`)
+- Bug in :meth:`RollingGroupby.count` where a ``ValueError`` was raised when specifying the ``closed`` parameter (:issue:`35869`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/tests/window/test_grouper.py b/pandas/tests/window/test_grouper.py
index d69ee72a00aee..63bf731e95096 100644
--- a/pandas/tests/window/test_grouper.py
+++ b/pandas/tests/window/test_grouper.py
@@ -472,3 +472,35 @@ def test_groupby_rolling_no_sort(self):
             index=pd.MultiIndex.from_tuples([(2, 0), (1, 1)], names=["foo", None]),
         )
         tm.assert_frame_equal(result, expected)
+
+    def test_groupby_rolling_count_closed_on(self):
+        # GH 35869
+        df = pd.DataFrame(
+            {
+                "column1": range(6),
+                "column2": range(6),
+                "group": 3 * ["A", "B"],
+                "date": pd.date_range(end="20190101", periods=6),
+            }
+        )
+        result = (
+            df.groupby("group")
+            .rolling("3d", on="date", closed="left")["column1"]
+            .count()
+        )
+        expected = pd.Series(
+            [np.nan, 1.0, 1.0, np.nan, 1.0, 1.0],
+            name="column1",
+            index=pd.MultiIndex.from_tuples(
+                [
+                    ("A", pd.Timestamp("2018-12-27")),
+                    ("A", pd.Timestamp("2018-12-29")),
+                    ("A", pd.Timestamp("2018-12-31")),
+                    ("B", pd.Timestamp("2018-12-28")),
+                    ("B", pd.Timestamp("2018-12-30")),
+                    ("B", pd.Timestamp("2019-01-01")),
+                ],
+                names=["group", "date"],
+            ),
+        )
+        tm.assert_series_equal(result, expected)