diff --git a/doc/whats_new/v1.0.rst b/doc/whats_new/v1.0.rst
index 96bb2ddfa8f7d..d0174cc8857d6 100644
--- a/doc/whats_new/v1.0.rst
+++ b/doc/whats_new/v1.0.rst
@@ -263,6 +263,11 @@ Changelog
   :pr:`18649` by `Leandro Hermida <hermidalc>` and
   `Rodion Martynov <marrodion>`.
 
+- |Fix| The `fit` method of the successive halving parameter search 
+  (:class:`model_selection.HalvingGridSearchCV`, and
+  :class:`model_selection.HalvingRandomSearchCV`) now correctly handles the
+  `groups` parameter. :pr:`19847` by :user:`Xiaoyu Chai <xiaoyuchai>`.
+
 :mod:`sklearn.naive_bayes`
 ..........................
 
diff --git a/sklearn/model_selection/_search_successive_halving.py b/sklearn/model_selection/_search_successive_halving.py
index b522ce7fbda41..d27cd3b1823ca 100644
--- a/sklearn/model_selection/_search_successive_halving.py
+++ b/sklearn/model_selection/_search_successive_halving.py
@@ -210,7 +210,7 @@ def fit(self, X, y=None, groups=None, **fit_params):
 
         self._n_samples_orig = _num_samples(X)
 
-        super().fit(X, y=y, groups=None, **fit_params)
+        super().fit(X, y=y, groups=groups, **fit_params)
 
         # Set best_score_: BaseSearchCV does not set it, as refit is a callable
         self.best_score_ = (
diff --git a/sklearn/model_selection/tests/test_successive_halving.py b/sklearn/model_selection/tests/test_successive_halving.py
index 2c55f6aa6cd85..6660b35a934ba 100644
--- a/sklearn/model_selection/tests/test_successive_halving.py
+++ b/sklearn/model_selection/tests/test_successive_halving.py
@@ -7,9 +7,16 @@
 from sklearn.datasets import make_classification
 from sklearn.dummy import DummyClassifier
 from sklearn.experimental import enable_halving_search_cv  # noqa
+from sklearn.model_selection import StratifiedKFold
+from sklearn.model_selection import StratifiedShuffleSplit
+from sklearn.model_selection import LeaveOneGroupOut
+from sklearn.model_selection import LeavePGroupsOut
+from sklearn.model_selection import GroupKFold
+from sklearn.model_selection import GroupShuffleSplit
 from sklearn.model_selection import HalvingGridSearchCV
 from sklearn.model_selection import HalvingRandomSearchCV
 from sklearn.model_selection import KFold, ShuffleSplit
+from sklearn.svm import LinearSVC
 from sklearn.model_selection._search_successive_halving import (
     _SubsampleMetaSplitter, _top_k, _refit_callable)
 
@@ -562,3 +569,32 @@ def set_params(self, **params):
 
     assert (cv_results_df['params'] == passed_params).all()
     assert (cv_results_df['n_resources'] == passed_n_samples).all()
+
+
+@pytest.mark.parametrize('Est', (HalvingGridSearchCV, HalvingRandomSearchCV))
+def test_groups_support(Est):
+    # Check if ValueError (when groups is None) propagates to
+    # HalvingGridSearchCV and HalvingRandomSearchCV
+    # And also check if groups is correctly passed to the cv object
+    rng = np.random.RandomState(0)
+
+    X, y = make_classification(n_samples=50, n_classes=2, random_state=0)
+    groups = rng.randint(0, 3, 50)
+
+    clf = LinearSVC(random_state=0)
+    grid = {'C': [1]}
+
+    group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2),
+                 GroupKFold(n_splits=3), GroupShuffleSplit(random_state=0)]
+    error_msg = "The 'groups' parameter should not be None."
+    for cv in group_cvs:
+        gs = Est(clf, grid, cv=cv)
+        with pytest.raises(ValueError, match=error_msg):
+            gs.fit(X, y)
+        gs.fit(X, y, groups=groups)
+
+    non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit(random_state=0)]
+    for cv in non_group_cvs:
+        gs = Est(clf, grid, cv=cv)
+        # Should not raise an error
+        gs.fit(X, y)