diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index ba5334b2f4fa8..bdd83e2adefd6 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -458,8 +458,9 @@ Groupby/resample/rolling
 - Bug in :meth:`GroupBy.groups` with a datetime key in conjunction with another key produced incorrect number of group keys (:issue:`51158`)
 - Bug in :meth:`GroupBy.quantile` may implicitly sort the result index with ``sort=False`` (:issue:`53009`)
 - Bug in :meth:`GroupBy.var` failing to raise ``TypeError`` when called with datetime64, timedelta64 or :class:`PeriodDtype` values (:issue:`52128`, :issue:`53045`)
-- Bug in :meth:`SeriresGroupBy.nth` and :meth:`DataFrameGroupBy.nth` after performing column selection when using ``dropna="any"`` or ``dropna="all"`` would not subset columns (:issue:`53518`)
-- Bug in :meth:`SeriresGroupBy.nth` and :meth:`DataFrameGroupBy.nth` raised after performing column selection when using ``dropna="any"`` or ``dropna="all"`` resulted in rows being dropped (:issue:`53518`)
+- Bug in :meth:`SeriesGroupBy.nth` and :meth:`DataFrameGroupBy.nth` after performing column selection when using ``dropna="any"`` or ``dropna="all"`` would not subset columns (:issue:`53518`)
+- Bug in :meth:`SeriesGroupBy.nth` and :meth:`DataFrameGroupBy.nth` raised after performing column selection when using ``dropna="any"`` or ``dropna="all"`` resulted in rows being dropped (:issue:`53518`)
+- Bug in :meth:`SeriesGroupBy.sum` and :meth:`DataFrameGroupby.sum` summing ``np.inf + np.inf`` and ``(-np.inf) + (-np.inf)`` to ``np.nan`` (:issue:`53606`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index 61f448cbe0c3f..0baae23a4a71c 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -746,6 +746,13 @@ def group_sum(
                         y = val - compensation[lab, j]
                         t = sumx[lab, j] + y
                         compensation[lab, j] = t - sumx[lab, j] - y
+                        if compensation[lab, j] != compensation[lab, j]:
+                            # GH#53606
+                            # If val is +/- infinity compensation is NaN
+                            # which would lead to results being NaN instead
+                            # of +/- infinity. We cannot use util.is_nan
+                            # because of no gil
+                            compensation[lab, j] = 0
                         sumx[lab, j] = t
 
             _check_below_mincount(
diff --git a/pandas/tests/groupby/test_libgroupby.py b/pandas/tests/groupby/test_libgroupby.py
index d10bcf9053d1a..92c3b68d87fad 100644
--- a/pandas/tests/groupby/test_libgroupby.py
+++ b/pandas/tests/groupby/test_libgroupby.py
@@ -6,6 +6,7 @@
     group_cumprod,
     group_cumsum,
     group_mean,
+    group_sum,
     group_var,
 )
 
@@ -302,3 +303,29 @@ def test_cython_group_mean_Inf_at_begining_and_end():
         actual,
         expected,
     )
+
+
+@pytest.mark.parametrize(
+    "values, out",
+    [
+        ([[np.inf], [np.inf], [np.inf]], [[np.inf], [np.inf]]),
+        ([[np.inf], [np.inf], [-np.inf]], [[np.inf], [np.nan]]),
+        ([[np.inf], [-np.inf], [np.inf]], [[np.inf], [np.nan]]),
+        ([[np.inf], [-np.inf], [-np.inf]], [[np.inf], [-np.inf]]),
+    ],
+)
+def test_cython_group_sum_Inf_at_begining_and_end(values, out):
+    # GH #53606
+    actual = np.array([[np.nan], [np.nan]], dtype="float64")
+    counts = np.array([0, 0], dtype="int64")
+    data = np.array(values, dtype="float64")
+    labels = np.array([0, 1, 1], dtype=np.intp)
+
+    group_sum(actual, counts, data, labels, None, is_datetimelike=False)
+
+    expected = np.array(out, dtype="float64")
+
+    tm.assert_numpy_array_equal(
+        actual,
+        expected,
+    )