diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 728288b686b05..c9267a756bef3 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -780,6 +780,7 @@ Groupby/resample/rolling
 - :class:`core.window.ewm.ExponentialMovingWindow` now raises a ``NotImplementedError`` when specifying ``times`` with ``adjust=False`` due to an incorrect calculation (:issue:`40098`)
 - Bug in :meth:`Series.asfreq` and :meth:`DataFrame.asfreq` dropping rows when the index is not sorted (:issue:`39805`)
 - Bug in aggregation functions for :class:`DataFrame` not respecting ``numeric_only`` argument when ``level`` keyword was given (:issue:`40660`)
+- Bug in :class:`core.window.RollingGroupby` where ``as_index=False`` argument in ``groupby`` was ignored (:issue:`39433`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index de5a65108a5cc..d10001c153bd2 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1920,6 +1920,7 @@ def rolling(self, *args, **kwargs):
             self._selected_obj,
             *args,
             _grouper=self.grouper,
+            _as_index=self.as_index,
             **kwargs,
         )
 
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index bdb7078334163..33b1ceee6e529 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -544,11 +544,13 @@ def __init__(
         obj: FrameOrSeries,
         *args,
         _grouper=None,
+        _as_index=True,
         **kwargs,
     ):
         if _grouper is None:
             raise ValueError("Must pass a Grouper object.")
         self._grouper = _grouper
+        self._as_index = _as_index
         # GH 32262: It's convention to keep the grouping column in
         # groupby.<agg_func>, but unexpected to users in
         # groupby.rolling.<agg_func>
@@ -610,6 +612,8 @@ def _apply(
         )
 
         result.index = result_index
+        if not self._as_index:
+            result = result.reset_index(level=list(range(len(groupby_keys))))
         return result
 
     def _apply_pairwise(
diff --git a/pandas/tests/window/test_groupby.py b/pandas/tests/window/test_groupby.py
index dd988a4abd9e1..51a6288598c32 100644
--- a/pandas/tests/window/test_groupby.py
+++ b/pandas/tests/window/test_groupby.py
@@ -732,6 +732,49 @@ def test_groupby_level(self):
         )
         tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "by, expected_data",
+        [
+            [["id"], {"num": [100.0, 150.0, 150.0, 200.0]}],
+            [
+                ["id", "index"],
+                {
+                    "date": [
+                        Timestamp("2018-01-01"),
+                        Timestamp("2018-01-02"),
+                        Timestamp("2018-01-01"),
+                        Timestamp("2018-01-02"),
+                    ],
+                    "num": [100.0, 200.0, 150.0, 250.0],
+                },
+            ],
+        ],
+    )
+    def test_as_index_false(self, by, expected_data):
+        # GH 39433
+        data = [
+            ["A", "2018-01-01", 100.0],
+            ["A", "2018-01-02", 200.0],
+            ["B", "2018-01-01", 150.0],
+            ["B", "2018-01-02", 250.0],
+        ]
+        df = DataFrame(data, columns=["id", "date", "num"])
+        df["date"] = to_datetime(df["date"])
+        df = df.set_index(["date"])
+
+        gp_by = [getattr(df, attr) for attr in by]
+        result = (
+            df.groupby(gp_by, as_index=False).rolling(window=2, min_periods=1).mean()
+        )
+
+        expected = {"id": ["A", "A", "B", "B"]}
+        expected.update(expected_data)
+        expected = DataFrame(
+            expected,
+            index=df.index,
+        )
+        tm.assert_frame_equal(result, expected)
+
 
 class TestExpanding:
     def setup_method(self):