diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index c0d1405e92518..b56ae569df9a5 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -26,7 +26,10 @@ from numpy cimport (
     uint32_t,
     uint64_t,
 )
-from numpy.math cimport NAN
+from numpy.math cimport (
+    NAN,
+    isinf,
+)
 
 cnp.import_array()
 
@@ -51,7 +54,14 @@ from pandas._libs.missing cimport checknull
 cdef int64_t NPY_NAT = get_nat()
 _int64_max = np.iinfo(np.int64).max
 
-cdef float64_t NaN = <float64_t>np.NaN
+cdef:
+    float32_t MINfloat32 = np.NINF
+    float64_t MINfloat64 = np.NINF
+
+    float32_t MAXfloat32 = np.inf
+    float64_t MAXfloat64 = np.inf
+
+    float64_t NaN = <float64_t>np.NaN
 
 cdef enum InterpolationEnumType:
     INTERPOLATION_LINEAR,
@@ -251,13 +261,18 @@ def group_cumsum(numeric_t[:, ::1] out,
 
                 # For floats, use Kahan summation to reduce floating-point
                 # error (https://en.wikipedia.org/wiki/Kahan_summation_algorithm)
-                if numeric_t == float32_t or numeric_t == float64_t:
+                if numeric_t is float32_t or numeric_t is float64_t:
                     if val == val:
-                        y = val - compensation[lab, j]
-                        t = accum[lab, j] + y
-                        compensation[lab, j] = t - accum[lab, j] - y
-                        accum[lab, j] = t
-                        out[i, j] = t
+                        # if val or accum are inf/-inf don't use kahan
+                        if isinf(val) or isinf(accum[lab, j]):
+                            accum[lab, j] += val
+                            out[i, j] = accum[lab, j]
+                        else:
+                            y = val - compensation[lab, j]
+                            t = accum[lab, j] + y
+                            compensation[lab, j] = t - accum[lab, j] - y
+                            accum[lab, j] = t
+                            out[i, j] = t
                     else:
                         out[i, j] = NaN
                         if not skipna:
@@ -557,6 +572,9 @@ def group_add(add_t[:, ::1] out,
                 for j in range(K):
                     val = values[i, j]
 
+                    if (val == MAXfloat64) or (val == MINfloat64):
+                        sumx[lab, j] = val
+                        break
                     # not nan
                     # With dt64/td64 values, values have been cast to float64
                     #  instead if int64 for group_add, but the logic
diff --git a/pandas/_libs/window/aggregations.pyx b/pandas/_libs/window/aggregations.pyx
index be8bb61092362..5622460616fbb 100644
--- a/pandas/_libs/window/aggregations.pyx
+++ b/pandas/_libs/window/aggregations.pyx
@@ -100,6 +100,10 @@ cdef inline void add_sum(float64_t val, int64_t *nobs, float64_t *sum_x,
         t = sum_x[0] + y
         compensation[0] = t - sum_x[0] - y
         sum_x[0] = t
+    if (val == MINfloat64) or (val == MAXfloat64):
+        sum_x[0] = val
+        nobs[0] = nobs[0] + 1
+        compensation[0] = 0
 
 
 cdef inline void remove_sum(float64_t val, int64_t *nobs, float64_t *sum_x,
@@ -116,6 +120,10 @@ cdef inline void remove_sum(float64_t val, int64_t *nobs, float64_t *sum_x,
         t = sum_x[0] + y
         compensation[0] = t - sum_x[0] - y
         sum_x[0] = t
+    if (val == MINfloat64) or (val == MAXfloat64):
+        sum_x[0] = val
+        nobs[0] = nobs[0] - 1
+        compensation[0] = 0
 
 
 def roll_sum(const float64_t[:] values, ndarray[int64_t] start,
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index 39a3e82fc2d98..18f4d11e839ba 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -1186,3 +1186,31 @@ def test_groupby_sum_timedelta_with_nat():
     res = gb["b"].sum(min_count=2)
     expected = Series([td3, pd.NaT], dtype="m8[ns]", name="b", index=expected.index)
     tm.assert_series_equal(res, expected)
+
+
+def test_sum_with_nan_inf():
+    df = DataFrame(
+        {"a": ["hello", "hello", "world", "world"], "b": [np.inf, 10, np.nan, 10]}
+    )
+    gb = df.groupby("a")
+    result = gb.sum()
+    expected = DataFrame(
+        [np.inf, 10], index=Index(["hello", "world"], name="a"), columns=["b"]
+    )
+    tm.assert_frame_equal(result, expected)
+
+
+def test_cumsum_inf():
+    ser = Series([np.inf, 1, 1])
+
+    result = ser.groupby([1, 1, 1]).cumsum()
+    expected = Series([np.inf, np.inf, np.inf])
+    tm.assert_series_equal(result, expected)
+
+
+def test_cumsum_ninf_inf():
+    ser = Series([np.inf, 1, 1, -np.inf, 1])
+
+    result = ser.groupby([1, 1, 1, 1, 1]).cumsum()
+    expected = Series([np.inf, np.inf, np.inf, np.nan, np.nan])
+    tm.assert_series_equal(result, expected)