diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 32faf7115f0fd..e81bc57317c89 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -359,6 +359,7 @@ Datetimelike
 - Bug in :class:`Series` and :class:`DataFrame` repr where ``np.datetime64('NaT')`` and ``np.timedelta64('NaT')`` with ``dtype=object`` would be represented as ``NaN`` (:issue:`25445`)
 - Bug in :func:`to_datetime` which does not replace the invalid argument with ``NaT`` when error is set to coerce (:issue:`26122`)
 - Bug in adding :class:`DateOffset` with nonzero month to :class:`DatetimeIndex` would raise ``ValueError`` (:issue:`26258`)
+- Bug in :func:`to_datetime` which raises unhandled ``OverflowError`` when called with mix of invalid dates and ``NaN`` values with ``format='%Y%m%d'`` and ``error='coerce'`` (:issue:`25512`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/tools/datetimes.py b/pandas/core/tools/datetimes.py
index 817d539d4ad6f..a39b65ab72aa8 100644
--- a/pandas/core/tools/datetimes.py
+++ b/pandas/core/tools/datetimes.py
@@ -775,21 +775,21 @@ def calc_with_mask(carg, mask):
     # try intlike / strings that are ints
     try:
         return calc(arg.astype(np.int64))
-    except ValueError:
+    except (ValueError, OverflowError):
         pass
 
     # a float with actual np.nan
     try:
         carg = arg.astype(np.float64)
         return calc_with_mask(carg, notna(carg))
-    except ValueError:
+    except (ValueError, OverflowError):
         pass
 
     # string with NaN-like
     try:
         mask = ~algorithms.isin(arg, list(tslib.nat_strings))
         return calc_with_mask(arg, mask)
-    except ValueError:
+    except (ValueError, OverflowError):
         pass
 
     return None
diff --git a/pandas/tests/indexes/datetimes/test_tools.py b/pandas/tests/indexes/datetimes/test_tools.py
index d62d8d1276fec..c507c31ee54dd 100644
--- a/pandas/tests/indexes/datetimes/test_tools.py
+++ b/pandas/tests/indexes/datetimes/test_tools.py
@@ -96,6 +96,25 @@ def test_to_datetime_format_YYYYMMDD(self, cache):
         result = pd.to_datetime(s, format='%Y%m%d', errors='coerce',
                                 cache=cache)
         expected = Series(['20121231', '20141231', 'NaT'], dtype='M8[ns]')
+        tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize("input_s, expected", [
+        # NaN before strings with invalid date values
+        [Series(['19801222', np.nan, '20010012', '10019999']),
+         Series([Timestamp('19801222'), np.nan, np.nan, np.nan])],
+        # NaN after strings with invalid date values
+        [Series(['19801222', '20010012', '10019999', np.nan]),
+         Series([Timestamp('19801222'), np.nan, np.nan, np.nan])],
+        # NaN before integers with invalid date values
+        [Series([20190813, np.nan, 20010012, 20019999]),
+         Series([Timestamp('20190813'), np.nan, np.nan, np.nan])],
+        # NaN after integers with invalid date values
+        [Series([20190813, 20010012, np.nan, 20019999]),
+         Series([Timestamp('20190813'), np.nan, np.nan, np.nan])]])
+    def test_to_datetime_format_YYYYMMDD_overflow(self, input_s, expected):
+        # GH 25512
+        # format='%Y%m%d', errors='coerce'
+        result = pd.to_datetime(input_s, format='%Y%m%d', errors='coerce')
         assert_series_equal(result, expected)
 
     @pytest.mark.parametrize('cache', [True, False])