diff --git a/doc/source/whatsnew/v0.19.0.txt b/doc/source/whatsnew/v0.19.0.txt
index ec37b6d6f5f13..21dd56966f098 100644
--- a/doc/source/whatsnew/v0.19.0.txt
+++ b/doc/source/whatsnew/v0.19.0.txt
@@ -513,6 +513,7 @@ Other enhancements
 - ``Timestamp``, ``Period``, ``DatetimeIndex``, ``PeriodIndex`` and ``.dt`` accessor have gained a ``.is_leap_year`` property to check whether the date belongs to a leap year. (:issue:`13727`)
 - ``astype()`` will now accept a dict of column name to data types mapping as the ``dtype`` argument. (:issue:`12086`)
 - The ``pd.read_json`` and ``DataFrame.to_json`` has gained support for reading and writing json lines with ``lines`` option see :ref:`Line delimited json <io.jsonl>` (:issue:`9180`)
+- `Series.sort_index`` will now accept kwargs ``kind`` and ``na_position`` (:issue:`13589`)
 
 .. _whatsnew_0190.api:
 
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 2f78c9acf7972..cf2762dc49976 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -2022,6 +2022,9 @@ def sort_values(self, by, axis=0, ascending=True, inplace=False,
             Sort ascending vs. descending
         inplace : bool, default False
             if True, perform operation in-place
+        sort_remaining : bool, default True
+            if true and sorting by level and index is multilevel, sort by other
+            levels too (in order) after sorting by specified level
         kind : {'quicksort', 'mergesort', 'heapsort'}, default 'quicksort'
              Choice of sorting algorithm. See also ndarray.np.sort for more
              information.  `mergesort` is the only stable algorithm. For
@@ -2029,9 +2032,6 @@ def sort_values(self, by, axis=0, ascending=True, inplace=False,
              column or label.
         na_position : {'first', 'last'}, default 'last'
              `first` puts NaNs at the beginning, `last` puts NaNs at the end
-        sort_remaining : bool, default True
-            if true and sorting by level and index is multilevel, sort by other
-            levels too (in order) after sorting by specified level
 
         Returns
         -------
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 8379c8bcdcae8..6d8753df5b3a2 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -1773,7 +1773,7 @@ def _try_kind_sort(arr):
 
     @Appender(generic._shared_docs['sort_index'] % _shared_doc_kwargs)
     def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
-                   sort_remaining=True):
+                   kind='quicksort', na_position='last', sort_remaining=True):
 
         axis = self._get_axis_number(axis)
         index = self.index
@@ -1782,12 +1782,15 @@ def sort_index(self, axis=0, level=None, ascending=True, inplace=False,
                                                  sort_remaining=sort_remaining)
         elif isinstance(index, MultiIndex):
             from pandas.core.groupby import _lexsort_indexer
-            indexer = _lexsort_indexer(index.labels, orders=ascending)
+            indexer = _lexsort_indexer(index.labels, orders=ascending,
+                                       na_position=na_position)
             indexer = _ensure_platform_int(indexer)
             new_index = index.take(indexer)
         else:
             new_index, indexer = index.sort_values(return_indexer=True,
-                                                   ascending=ascending)
+                                                   ascending=ascending,
+                                                   kind=kind,
+                                                   na_position=na_position)
 
         new_values = self._values.take(indexer)
         result = self._constructor(new_values, index=new_index)
diff --git a/pandas/tests/series/test_sorting.py b/pandas/tests/series/test_sorting.py
index 826201adbdb50..6af284417a15a 100644
--- a/pandas/tests/series/test_sorting.py
+++ b/pandas/tests/series/test_sorting.py
@@ -5,7 +5,7 @@
 
 from pandas import (DataFrame, Series, MultiIndex)
 
-from pandas.util.testing import (assert_series_equal, assert_almost_equal)
+from pandas.util.testing import (assert_series_equal, assert_almost_equal, assertRaisesRegexp)
 import pandas.util.testing as tm
 
 from .common import TestData
@@ -144,3 +144,22 @@ def test_sort_index_multiindex(self):
         # rows share same level='A': sort has no effect without remaining lvls
         res = s.sort_index(level='A', sort_remaining=False)
         assert_series_equal(s, res)
+
+    def test_sort_index_nan(self):
+
+        # GH13729
+        ser = Series(['A', np.nan, 'C', 'D'], [1, 2, 0, np.nan])
+
+        # na_position='last', kind='quicksort'
+        result = ser.sort_index(kind='quicksort', na_position='last')
+        expected = Series(['C', 'A', np.nan, 'D'], [0, 1, 2, np.nan])
+        assert_series_equal(result, expected)
+
+        # na_position='first'
+        result = ser.sort_index(na_position='first')
+        expected = Series(['D', 'C', 'A', np.nan], [np.nan, 0, 1, 2])
+        assert_series_equal(result, expected)
+
+        # invalid argument
+        assertRaisesRegexp(TypeError, 'got an unexpected keyword argument',
+                            ser.sort_index, arg='first')