diff --git a/doc/source/release.rst b/doc/source/release.rst
index 7c09c2a6f16ac..62d3201eb3a58 100644
--- a/doc/source/release.rst
+++ b/doc/source/release.rst
@@ -48,6 +48,8 @@ pandas 0.13
     with a different block ordering (:issue:`4096`)
   - The ``by`` argument now works correctly with the ``layout`` argument
     (:issue:`4102`, :issue:`4014`) in ``*.hist`` plotting methods
+  - Fixed bug in ``PeriodIndex.map`` where using ``str`` would return the str
+    representation of the index (:issue:`4136`)
 
 pandas 0.12
 ===========
diff --git a/doc/source/v0.13.0.txt b/doc/source/v0.13.0.txt
index 7f63c545c5664..a8b61f338d044 100644
--- a/doc/source/v0.13.0.txt
+++ b/doc/source/v0.13.0.txt
@@ -24,6 +24,9 @@ Bug Fixes
   - The ``by`` argument now works correctly with the ``layout`` argument
     (:issue:`4102`, :issue:`4014`) in ``*.hist`` plotting methods
 
+  - Fixed bug in ``PeriodIndex.map`` where using ``str`` would return the str
+    representation of the index (:issue:`4136`)
+
 See the :ref:`full release notes
 <release>` or issue tracker
 on GitHub for a complete list.
diff --git a/pandas/tseries/period.py b/pandas/tseries/period.py
index 2db32b14e2eb3..4fec590dddd14 100644
--- a/pandas/tseries/period.py
+++ b/pandas/tseries/period.py
@@ -469,7 +469,6 @@ def dt64arr_to_periodarr(data, freq, tz):
 
 # --- Period index sketch
 
-
 def _period_index_cmp(opname):
     """
     Wrap comparison operations to convert datetime-like to datetime64
@@ -493,6 +492,7 @@ def wrapper(self, other):
         return result
     return wrapper
 
+
 class PeriodIndex(Int64Index):
     """
     Immutable ndarray holding ordinal values indicating regular periods in
@@ -791,10 +791,12 @@ def to_datetime(self, dayfirst=False):
     # Especially important for group-by functionality
     def map(self, f):
         try:
-            return f(self)
-        except:
-            values = self._get_object_array()
-            return _algos.arrmap_object(values, f)
+            result = f(self)
+            if not isinstance(result, np.ndarray):
+                raise TypeError
+            return result
+        except Exception:
+            return _algos.arrmap_object(self.asobject, f)
 
     def _get_object_array(self):
         freq = self.freq
@@ -1169,6 +1171,7 @@ def __setstate__(self, state):
         else:  # pragma: no cover
             np.ndarray.__setstate__(self, state)
 
+
 def _get_ordinal_range(start, end, periods, freq):
     if com._count_not_none(start, end, periods) < 2:
         raise ValueError('Must specify 2 of start, end, periods')
diff --git a/pandas/tseries/tests/test_period.py b/pandas/tseries/tests/test_period.py
index 01c984ec2b07d..9fd5e6bf5f3e9 100644
--- a/pandas/tseries/tests/test_period.py
+++ b/pandas/tseries/tests/test_period.py
@@ -27,6 +27,7 @@
 from pandas import Series, TimeSeries, DataFrame
 from pandas.util.testing import assert_series_equal, assert_almost_equal
 import pandas.util.testing as tm
+from pandas.util import py3compat
 from numpy.testing import assert_array_equal
 
 
@@ -1990,7 +1991,30 @@ def test_map(self):
 
         result = index.map(lambda x: x.ordinal)
         exp = [x.ordinal for x in index]
-        self.assert_(np.array_equal(result, exp))
+        assert_array_equal(result, exp)
+
+    def test_map_with_string_constructor(self):
+        raw = [2005, 2007, 2009]
+        index = PeriodIndex(raw, freq='A')
+        types = str,
+        if not py3compat.PY3:
+            types += unicode,
+
+        for t in types:
+            expected = np.array(map(t, raw), dtype=object)
+            res = index.map(t)
+
+            # should return an array
+            self.assert_(isinstance(res, np.ndarray))
+
+            # preserve element types
+            self.assert_(all(isinstance(resi, t) for resi in res))
+
+            # dtype should be object
+            self.assertEqual(res.dtype, np.dtype('object').type)
+
+            # lastly, values should compare equal
+            assert_array_equal(res, expected)
 
     def test_convert_array_of_periods(self):
         rng = period_range('1/1/2000', periods=20, freq='D')