diff --git a/doc/source/whatsnew/v0.25.1.rst b/doc/source/whatsnew/v0.25.1.rst
index f4308684e286a..cd0a4d0c4c3c7 100644
--- a/doc/source/whatsnew/v0.25.1.rst
+++ b/doc/source/whatsnew/v0.25.1.rst
@@ -85,7 +85,7 @@ Indexing
 - Bug in partial-string indexing returning a NumPy array rather than a ``Series`` when indexing with a scalar like ``.loc['2015']`` (:issue:`27516`)
 - Break reference cycle involving :class:`Index` and other index classes to allow garbage collection of index objects without running the GC. (:issue:`27585`, :issue:`27840`)
 - Fix regression in assigning values to a single column of a DataFrame with a ``MultiIndex`` columns (:issue:`27841`).
--
+- `IndexError` would not raised if group keys are nan value (:issue:`20519`)
 
 Missing
 ^^^^^^^
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 5f17dde01d2c4..1e2796562f29f 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -873,7 +873,13 @@ def _assert_take_fillable(
                 values, indices, allow_fill=allow_fill, fill_value=na_value
             )
         else:
-            taken = values.take(indices)
+            try:
+                taken = values.take(indices)
+            except IndexError:
+                if not values.tolist():
+                    return []
+                else:
+                    raise
         return taken
 
     _index_shared_docs[
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index d1ed79118d2fa..1848c7e791f73 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -2240,6 +2240,25 @@ def test_groupby(self):
 
         tm.assert_dict_equal(result, expected)
 
+    def test_groupby_nan_index_value(self):
+        df = pd.DataFrame([["x", np.nan, 1]], columns=["A", "B", "C"]).set_index(
+            ["A", "B"]
+        )
+        result = df.groupby(level=["A", "B"]).C.sum()
+        s = Series([])
+        s.name = "C"
+        expected = s.astype("int64")
+        tm.assert_series_equal(result, expected)
+
+        df = pd.DataFrame(
+            [["x", np.nan, 1, 2], [None, "y", 3, 4]], columns=["A", "B", "C", "D"]
+        ).set_index(["A", "B", "C"])
+        result = df.groupby(level=["A", "B"]).D.sum()
+        s = Series([])
+        s.name = "D"
+        expected = s.astype("int64")
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize(
         "mi,expected",
         [