diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 686c5ad0165e7..9d33c651ef283 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -149,10 +149,9 @@ Missing
 MultiIndex
 ^^^^^^^^^^
 
+- Bug in which incorrect exception raised by :meth:`pd.Timedelta` when testing the membership of :class:`MultiIndex` (:issue:`24570`)
 -
 -
--
-
 
 I/O
 ^^^
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index efb77b5d155a1..c19b6f61f2caa 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -840,7 +840,7 @@ def __contains__(self, key):
         try:
             self.get_loc(key)
             return True
-        except (LookupError, TypeError):
+        except (LookupError, TypeError, ValueError):
             return False
 
     contains = __contains__
diff --git a/pandas/tests/indexing/multiindex/test_multiindex.py b/pandas/tests/indexing/multiindex/test_multiindex.py
index 4f5517f89e852..ccf017489e046 100644
--- a/pandas/tests/indexing/multiindex/test_multiindex.py
+++ b/pandas/tests/indexing/multiindex/test_multiindex.py
@@ -84,3 +84,11 @@ def test_multi_nan_indexing(self):
                                           name='a'),
                                     Index(['C1', 'C2', 'C3', 'C4'], name='b')])
         tm.assert_frame_equal(result, expected)
+
+    def test_contains(self):
+        # GH 24570
+        tx = pd.timedelta_range('09:30:00', '16:00:00', freq='30 min')
+        idx = MultiIndex.from_arrays([tx, np.arange(len(tx))])
+        assert tx[0] in idx
+        assert 'element_not_exit' not in idx
+        assert '0 day 09:30:00' in idx