diff --git a/pandas/tests/arithmetic/test_datetime64.py b/pandas/tests/arithmetic/test_datetime64.py
index a3fa4e6b88256..b19cc61a2999e 100644
--- a/pandas/tests/arithmetic/test_datetime64.py
+++ b/pandas/tests/arithmetic/test_datetime64.py
@@ -1764,6 +1764,7 @@ def test_dt64_with_DateOffsets_relativedelta(klass):
     'MonthBegin', 'MonthEnd',
     'SemiMonthEnd', 'SemiMonthBegin',
     'Week', ('Week', {'weekday': 3}),
+    'Week', ('Week', {'weekday': 6}),
     'BusinessDay', 'BDay', 'QuarterEnd', 'QuarterBegin',
     'CustomBusinessDay', 'CDay', 'CBMonthEnd',
     'CBMonthBegin', 'BMonthBegin', 'BMonthEnd',
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index d4a8211c17b87..0a9931c46bbd5 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -1313,7 +1313,7 @@ def _end_apply_index(self, dtindex):
         base_period = dtindex.to_period(base)
         if self.n > 0:
             # when adding, dates on end roll to next
-            normed = dtindex - off
+            normed = dtindex - off + Timedelta(1, 'D') - Timedelta(1, 'ns')
             roll = np.where(base_period.to_timestamp(how='end') == normed,
                             self.n, self.n - 1)
         else: