diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 8d9e1e9958d23..3774ed2f32c13 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -268,6 +268,7 @@ Other enhancements
 - :meth:`read_csv` and :meth:`read_json` expose the argument ``encoding_errors`` to control how encoding errors are handled (:issue:`39450`)
 - :meth:`.GroupBy.any` and :meth:`.GroupBy.all` use Kleene logic with nullable data types (:issue:`37506`)
 - :meth:`.GroupBy.any` and :meth:`.GroupBy.all` return a ``BooleanDtype`` for columns with nullable data types (:issue:`33449`)
+- :meth:`.GroupBy.any` and :meth:`.GroupBy.all` raising with ``object`` data containing ``pd.NA`` even when ``skipna=True`` (:issue:`37501`)
 - :meth:`.GroupBy.rank` now supports object-dtype data (:issue:`38278`)
 - Constructing a :class:`DataFrame` or :class:`Series` with the ``data`` argument being a Python iterable that is *not* a NumPy ``ndarray`` consisting of NumPy scalars will now result in a dtype with a precision the maximum of the NumPy scalars; this was already the case when ``data`` is a NumPy ``ndarray`` (:issue:`40908`)
 - Add keyword ``sort`` to :func:`pivot_table` to allow non-sorting of the result (:issue:`39143`)
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index f694dcce809ea..0080791a51a4b 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1519,7 +1519,11 @@ def _bool_agg(self, val_test, skipna):
 
         def objs_to_bool(vals: ArrayLike) -> tuple[np.ndarray, type]:
             if is_object_dtype(vals):
-                vals = np.array([bool(x) for x in vals])
+                # GH#37501: don't raise on pd.NA when skipna=True
+                if skipna:
+                    vals = np.array([bool(x) if not isna(x) else True for x in vals])
+                else:
+                    vals = np.array([bool(x) for x in vals])
             elif isinstance(vals, BaseMaskedArray):
                 vals = vals._data.astype(bool, copy=False)
             else:
diff --git a/pandas/tests/groupby/test_any_all.py b/pandas/tests/groupby/test_any_all.py
index d4f80aa0e51d4..13232d454a48c 100644
--- a/pandas/tests/groupby/test_any_all.py
+++ b/pandas/tests/groupby/test_any_all.py
@@ -152,3 +152,29 @@ def test_masked_bool_aggs_skipna(bool_agg_func, dtype, skipna, frame_or_series):
 
     result = obj.groupby([1, 1]).agg(bool_agg_func, skipna=skipna)
     tm.assert_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "bool_agg_func,data,expected_res",
+    [
+        ("any", [pd.NA, np.nan], False),
+        ("any", [pd.NA, 1, np.nan], True),
+        ("all", [pd.NA, pd.NaT], True),
+        ("all", [pd.NA, False, pd.NaT], False),
+    ],
+)
+def test_object_type_missing_vals(bool_agg_func, data, expected_res, frame_or_series):
+    # GH#37501
+    obj = frame_or_series(data, dtype=object)
+    result = obj.groupby([1] * len(data)).agg(bool_agg_func)
+    expected = frame_or_series([expected_res], index=[1], dtype="bool")
+    tm.assert_equal(result, expected)
+
+
+@pytest.mark.filterwarnings("ignore:Dropping invalid columns:FutureWarning")
+@pytest.mark.parametrize("bool_agg_func", ["any", "all"])
+def test_object_NA_raises_with_skipna_false(bool_agg_func):
+    # GH#37501
+    ser = Series([pd.NA], dtype=object)
+    with pytest.raises(TypeError, match="boolean value of NA is ambiguous"):
+        ser.groupby([1]).agg(bool_agg_func, skipna=False)