diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index affe019d0ac86..82d603cfb8c15 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -76,6 +76,7 @@ Bug fixes
 
 - Fix bug in :meth:`DataFrame.convert_dtypes` for columns that were already using the ``"string"`` dtype (:issue:`31731`).
 - Fixed bug in setting values using a slice indexer with string dtype (:issue:`31772`)
+- Fixed bug where :meth:`GroupBy.first` and :meth:`GroupBy.last` would raise a ``TypeError`` when groups contained ``pd.NA`` in a column of object dtype (:issue:`32123`)
 - Fix bug in :meth:`Series.convert_dtypes` for series with mix of integers and strings (:issue:`32117`)
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index edc44f1c94589..27b3095d8cb4f 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -22,6 +22,8 @@ from pandas._libs.algos cimport (swap, TiebreakEnumType, TIEBREAK_AVERAGE,
 from pandas._libs.algos import (take_2d_axis1_float64_float64,
                                 groupsort_indexer, tiebreakers)
 
+from pandas._libs.missing cimport checknull
+
 cdef int64_t NPY_NAT = get_nat()
 _int64_max = np.iinfo(np.int64).max
 
@@ -887,7 +889,7 @@ def group_last(rank_t[:, :] out,
             for j in range(K):
                 val = values[i, j]
 
-                if val == val:
+                if not checknull(val):
                     # NB: use _treat_as_na here once
                     #  conditional-nogil is available.
                     nobs[lab, j] += 1
@@ -976,7 +978,7 @@ def group_nth(rank_t[:, :] out,
             for j in range(K):
                 val = values[i, j]
 
-                if val == val:
+                if not checknull(val):
                     # NB: use _treat_as_na here once
                     #  conditional-nogil is available.
                     nobs[lab, j] += 1
diff --git a/pandas/tests/groupby/test_nth.py b/pandas/tests/groupby/test_nth.py
index 0f850f2e94581..b1476f1059d84 100644
--- a/pandas/tests/groupby/test_nth.py
+++ b/pandas/tests/groupby/test_nth.py
@@ -54,6 +54,46 @@ def test_first_last_nth(df):
     tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize("method", ["first", "last"])
+def test_first_last_with_na_object(method, nulls_fixture):
+    # https://github.com/pandas-dev/pandas/issues/32123
+    groups = pd.DataFrame({"a": [1, 1, 2, 2], "b": [1, 2, 3, nulls_fixture]}).groupby(
+        "a"
+    )
+    result = getattr(groups, method)()
+
+    if method == "first":
+        values = [1, 3]
+    else:
+        values = [2, 3]
+
+    values = np.array(values, dtype=result["b"].dtype)
+    idx = pd.Index([1, 2], name="a")
+    expected = pd.DataFrame({"b": values}, index=idx)
+
+    tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("index", [0, -1])
+def test_nth_with_na_object(index, nulls_fixture):
+    # https://github.com/pandas-dev/pandas/issues/32123
+    groups = pd.DataFrame({"a": [1, 1, 2, 2], "b": [1, 2, 3, nulls_fixture]}).groupby(
+        "a"
+    )
+    result = groups.nth(index)
+
+    if index == 0:
+        values = [1, 3]
+    else:
+        values = [2, nulls_fixture]
+
+    values = np.array(values, dtype=result["b"].dtype)
+    idx = pd.Index([1, 2], name="a")
+    expected = pd.DataFrame({"b": values}, index=idx)
+
+    tm.assert_frame_equal(result, expected)
+
+
 def test_first_last_nth_dtypes(df_mixed_floats):
 
     df = df_mixed_floats.copy()