diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 814dbe999d5c1..43b117a2bc35f 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -1162,6 +1162,8 @@ Other
 - Bug in :meth:`DataFrame.__dir__` caused a segfault when using unicode surrogates in a column name (:issue:`25509`)
 - Bug in :meth:`DataFrame.plot.scatter` caused an error when plotting variable marker sizes (:issue:`32904`)
 - :class:`IntegerArray` now implements the ``sum`` operation (:issue:`33172`)
+- Bug in :meth:`DataFrame.equals` and :meth:`Series.equals` in allowing subclasses
+  to be equal (:issue:`34402`).
 - Bug in :class:`Tick` comparisons raising ``TypeError`` when comparing against timedelta-like objects (:issue:`34088`)
 - Bug in :class:`Tick` multiplication raising ``TypeError`` when multiplying by a float (:issue:`34486`)
 - Passing a `set` as `names` argument to :func:`pandas.read_csv`, :func:`pandas.read_table`, or :func:`pandas.read_fwf` will raise ``ValueError: Names should be an ordered collection.`` (:issue:`34946`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index eb55369d83593..e46fde1f59f16 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -1278,7 +1278,7 @@ def equals(self, other):
         >>> df.equals(different_data_type)
         False
         """
-        if not isinstance(other, self._constructor):
+        if not (isinstance(other, type(self)) or isinstance(self, type(other))):
             return False
         return self._mgr.equals(other._mgr)
 
diff --git a/pandas/tests/frame/test_subclass.py b/pandas/tests/frame/test_subclass.py
index 08920cf7fceeb..2b462d5a10c51 100644
--- a/pandas/tests/frame/test_subclass.py
+++ b/pandas/tests/frame/test_subclass.py
@@ -696,3 +696,11 @@ def test_idxmax_preserves_subclass(self):
         df = tm.SubclassedDataFrame({"A": [1, 2, 3], "B": [4, 5, 6], "C": [7, 8, 9]})
         result = df.idxmax()
         assert isinstance(result, tm.SubclassedSeries)
+
+    def test_equals_subclass(self):
+        # https://github.com/pandas-dev/pandas/pull/34402
+        # allow subclass in both directions
+        df1 = pd.DataFrame({"a": [1, 2, 3]})
+        df2 = tm.SubclassedDataFrame({"a": [1, 2, 3]})
+        assert df1.equals(df2)
+        assert df2.equals(df1)
diff --git a/pandas/tests/series/test_subclass.py b/pandas/tests/series/test_subclass.py
index a596ed49c1df2..86330b7cc6993 100644
--- a/pandas/tests/series/test_subclass.py
+++ b/pandas/tests/series/test_subclass.py
@@ -51,3 +51,11 @@ def test_explode(self):
         s = tm.SubclassedSeries([[1, 2, 3], "foo", [], [3, 4]])
         result = s.explode()
         assert isinstance(result, tm.SubclassedSeries)
+
+    def test_equals(self):
+        # https://github.com/pandas-dev/pandas/pull/34402
+        # allow subclass in both directions
+        s1 = pd.Series([1, 2, 3])
+        s2 = tm.SubclassedSeries([1, 2, 3])
+        assert s1.equals(s2)
+        assert s2.equals(s1)