diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 00379c7e9d511..51735548db7d3 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -84,6 +84,7 @@ Other Enhancements
 - :meth:`Series.nlargest`, :meth:`Series.nsmallest`, :meth:`DataFrame.nlargest`, and :meth:`DataFrame.nsmallest` now accept the value ``"all"`` for the ``keep`` argument. This keeps all ties for the nth largest/smallest value (:issue:`16818`)
 - :class:`IntervalIndex` has gained the :meth:`~IntervalIndex.set_closed` method to change the existing ``closed`` value (:issue:`21670`)
 - :func:`~DataFrame.to_csv` and :func:`~DataFrame.to_json` now support ``compression='infer'`` to infer compression based on filename (:issue:`15008`)
+- :func:`Series.str.zfill()` now matches with standard string library zfill (:issue:`20868`)
 -
 
 .. _whatsnew_0240.api_breaking:
diff --git a/pandas/core/strings.py b/pandas/core/strings.py
index e4765c00f80fd..29990e0efa8af 100644
--- a/pandas/core/strings.py
+++ b/pandas/core/strings.py
@@ -2557,20 +2557,26 @@ def zfill(self, width):
 
         Note that ``10`` and ``NaN`` are not strings, therefore they are
         converted to ``NaN``. The minus sign in ``'-1'`` is treated as a
-        regular character and the zero is added to the left of it
+        special character and the zero is added to the right of it
         (:meth:`str.zfill` would have moved it to the left). ``1000``
         remains unchanged as it is longer than `width`.
 
         >>> s.str.zfill(3)
-        0     0-1
+        0     -01
         1     001
         2    1000
         3     NaN
         4     NaN
         dtype: object
         """
-        result = str_pad(self._data, width, side='left', fillchar='0')
-        return self._wrap_result(result)
+
+        if not is_integer(width):
+            msg = 'width must be of integer type, not {0}'
+            raise TypeError(msg.format(type(width).__name__))
+
+        f = lambda x: x.zfill(width)
+
+        return self._wrap_result(_na_map(f, self._data))
 
     @copy(str_slice)
     def slice(self, start=None, stop=None, step=None):
diff --git a/pandas/tests/test_strings.py b/pandas/tests/test_strings.py
index 9d008dfd25c90..8624cba57a354 100644
--- a/pandas/tests/test_strings.py
+++ b/pandas/tests/test_strings.py
@@ -2220,27 +2220,31 @@ def test_center_ljust_rjust_fillchar(self):
             result = values.str.rjust(5, fillchar=1)
 
     def test_zfill(self):
-        values = Series(['1', '22', 'aaa', '333', '45678'])
+        values = Series(['1', '+1', '-1', '22', 'aaa', '333', '45678'])
 
         result = values.str.zfill(5)
-        expected = Series(['00001', '00022', '00aaa', '00333', '45678'])
+        expected = Series(['00001', '+0001', '-0001', '00022', '00aaa',
+                           '00333', '45678'])
         tm.assert_series_equal(result, expected)
         expected = np.array([v.zfill(5) for v in values.values],
                             dtype=np.object_)
         tm.assert_numpy_array_equal(result.values, expected)
 
         result = values.str.zfill(3)
-        expected = Series(['001', '022', 'aaa', '333', '45678'])
+        expected = Series(['001', '+01', '-01', '022', 'aaa', '333', '45678'])
         tm.assert_series_equal(result, expected)
         expected = np.array([v.zfill(3) for v in values.values],
                             dtype=np.object_)
         tm.assert_numpy_array_equal(result.values, expected)
 
-        values = Series(['1', np.nan, 'aaa', np.nan, '45678'])
+        values = Series(['1', np.nan, 'aaa', np.nan, '45678', 10])
         result = values.str.zfill(5)
-        expected = Series(['00001', np.nan, '00aaa', np.nan, '45678'])
+        expected = Series(['00001', np.nan, '00aaa', np.nan, '45678', np.nan])
         tm.assert_series_equal(result, expected)
 
+        with tm.assert_raises_regex(TypeError, "width must be of integer"):
+            values.str.zfill('5')
+
     def test_split(self):
         values = Series(['a_b_c', 'c_d_e', NA, 'f_g_h'])