diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index d86c1b7911528..4202c01dfe551 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -156,7 +156,7 @@ Categorical
 Datetimelike
 ^^^^^^^^^^^^
 - Bug in :class:`DataFrame` and :class:`Series` constructors sometimes dropping nanoseconds from :class:`Timestamp` (resp. :class:`Timedelta`) ``data``, with ``dtype=datetime64[ns]`` (resp. ``timedelta64[ns]``) (:issue:`38032`)
--
+- Bug in :meth:`DataFrame.first` and :meth:`Series.first` returning two months for offset one month when first day is last calendar day (:issue:`29623`)
 -
 
 Timedelta
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 41cb76d88957e..e0b5df7e2cf0c 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -8420,7 +8420,12 @@ def first(self: FrameOrSeries, offset) -> FrameOrSeries:
             return self
 
         offset = to_offset(offset)
-        end_date = end = self.index[0] + offset
+        if not isinstance(offset, Tick) and offset.is_on_offset(self.index[0]):
+            # GH#29623 if first value is end of period, remove offset with n = 1
+            #  before adding the real offset
+            end_date = end = self.index[0] - offset.base + offset
+        else:
+            end_date = end = self.index[0] + offset
 
         # Tick-like, e.g. 3 weeks
         if isinstance(offset, Tick):
diff --git a/pandas/tests/frame/methods/test_first_and_last.py b/pandas/tests/frame/methods/test_first_and_last.py
index d21e1eee54e16..43469a093f827 100644
--- a/pandas/tests/frame/methods/test_first_and_last.py
+++ b/pandas/tests/frame/methods/test_first_and_last.py
@@ -3,7 +3,7 @@
 """
 import pytest
 
-from pandas import DataFrame
+from pandas import DataFrame, bdate_range
 import pandas._testing as tm
 
 
@@ -69,3 +69,22 @@ def test_last_subset(self, frame_or_series):
 
         result = ts[:0].last("3M")
         tm.assert_equal(result, ts[:0])
+
+    @pytest.mark.parametrize("start, periods", [("2010-03-31", 1), ("2010-03-30", 2)])
+    def test_first_with_first_day_last_of_month(self, frame_or_series, start, periods):
+        # GH#29623
+        x = frame_or_series([1] * 100, index=bdate_range(start, periods=100))
+        result = x.first("1M")
+        expected = frame_or_series(
+            [1] * periods, index=bdate_range(start, periods=periods)
+        )
+        tm.assert_equal(result, expected)
+
+    def test_first_with_first_day_end_of_frq_n_greater_one(self, frame_or_series):
+        # GH#29623
+        x = frame_or_series([1] * 100, index=bdate_range("2010-03-31", periods=100))
+        result = x.first("2M")
+        expected = frame_or_series(
+            [1] * 23, index=bdate_range("2010-03-31", "2010-04-30")
+        )
+        tm.assert_equal(result, expected)