diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index b061c4040096e..eed712ae7de0f 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -233,6 +233,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.intersection`, :meth:`DatetimeIndex.symmetric_difference`, :meth:`PeriodIndex.intersection`, :meth:`PeriodIndex.symmetric_difference` always returning object-dtype when operating with :class:`CategoricalIndex` (:issue:`38741`)
 - Bug in :meth:`Series.where` incorrectly casting ``datetime64`` values to ``int64`` (:issue:`37682`)
 - Bug in :class:`Categorical` incorrectly typecasting ``datetime`` object to ``Timestamp`` (:issue:`38878`)
+- Bug in :func:`date_range` incorrectly creating :class:`DatetimeIndex` containing ``NaT`` instead of raising ``OutOfBoundsDatetime`` in corner cases (:issue:`24124`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/arrays/_ranges.py b/pandas/core/arrays/_ranges.py
index 14b442bf71080..c001c57ffe757 100644
--- a/pandas/core/arrays/_ranges.py
+++ b/pandas/core/arrays/_ranges.py
@@ -7,7 +7,13 @@
 
 import numpy as np
 
-from pandas._libs.tslibs import BaseOffset, OutOfBoundsDatetime, Timedelta, Timestamp
+from pandas._libs.tslibs import (
+    BaseOffset,
+    OutOfBoundsDatetime,
+    Timedelta,
+    Timestamp,
+    iNaT,
+)
 
 
 def generate_regular_range(
@@ -150,7 +156,12 @@ def _generate_range_overflow_safe_signed(
         addend = np.int64(periods) * np.int64(stride)
         try:
             # easy case with no overflows
-            return np.int64(endpoint) + addend
+            result = np.int64(endpoint) + addend
+            if result == iNaT:
+                # Putting this into a DatetimeArray/TimedeltaArray
+                #  would incorrectly be interpreted as NaT
+                raise OverflowError
+            return result
         except (FloatingPointError, OverflowError):
             # with endpoint negative and addend positive we risk
             #  FloatingPointError; with reversed signed we risk OverflowError
diff --git a/pandas/tests/indexes/datetimes/test_date_range.py b/pandas/tests/indexes/datetimes/test_date_range.py
index 7c70b58318a11..b8def8072a3b7 100644
--- a/pandas/tests/indexes/datetimes/test_date_range.py
+++ b/pandas/tests/indexes/datetimes/test_date_range.py
@@ -15,7 +15,7 @@
 import pandas.util._test_decorators as td
 
 import pandas as pd
-from pandas import DatetimeIndex, Timestamp, bdate_range, date_range, offsets
+from pandas import DatetimeIndex, Timedelta, Timestamp, bdate_range, date_range, offsets
 import pandas._testing as tm
 from pandas.core.arrays.datetimes import generate_range
 
@@ -76,6 +76,13 @@ def test_date_range_timestamp_equiv_preserve_frequency(self):
 
 
 class TestDateRanges:
+    def test_date_range_near_implementation_bound(self):
+        # GH#???
+        freq = Timedelta(1)
+
+        with pytest.raises(OutOfBoundsDatetime, match="Cannot generate range with"):
+            date_range(end=Timestamp.min, periods=2, freq=freq)
+
     def test_date_range_nat(self):
         # GH#11587
         msg = "Neither `start` nor `end` can be NaT"