diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index db23bfdc8a5bd..00983485e782d 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -343,6 +343,7 @@ Other API changes
   See :ref:`units registration <whatsnew_1000.matplotlib_units>` for more.
 - :meth:`Series.dropna` has dropped its ``**kwargs`` argument in favor of a single ``how`` parameter.
   Supplying anything else than ``how`` to ``**kwargs`` raised a ``TypeError`` previously (:issue:`29388`)
+- :meth:`Series.interpolate` will issue a warning if using ``index`` or ``values`` method when index is not sorted. (:issue:`21037`)
 - When testing pandas, the new minimum required version of pytest is 5.0.1 (:issue:`29664`)
 -
 
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index 744cde95cb668..b6128d40850fe 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -1,6 +1,7 @@
 """
 Routines for filling missing data.
 """
+import warnings
 
 import numpy as np
 
@@ -21,6 +22,14 @@
 from pandas.core.dtypes.missing import isna
 
 
+class IndexNotSortedWarning(Warning):
+    """
+    Warning raised when index is not sorted and interpolate with an unsupported method.
+    """
+
+    pass
+
+
 def mask_missing(arr, values_to_mask):
     """
     Return a masking array of same size/shape as arr
@@ -277,6 +286,9 @@ def interpolate_1d(
                 inds = lib.maybe_convert_objects(inds)
         else:
             inds = xvalues
+        if not np.all(np.diff(inds) > 0):
+            msg = "interpolation method '%s' requires sorted index." % method
+            warnings.warn(msg, IndexNotSortedWarning)
         result[invalid] = np.interp(inds[invalid], inds[valid], yvalues[valid])
         result[preserve_nans] = np.nan
         return result
diff --git a/pandas/tests/series/test_missing.py b/pandas/tests/series/test_missing.py
index 81bf1edbe86df..b5d173f70d06a 100644
--- a/pandas/tests/series/test_missing.py
+++ b/pandas/tests/series/test_missing.py
@@ -20,6 +20,7 @@
     date_range,
     isna,
 )
+from pandas.core.missing import IndexNotSortedWarning
 import pandas.util.testing as tm
 
 
@@ -1655,3 +1656,11 @@ def test_interpolate_timedelta_index(self, interp_methods_ind):
             pytest.skip(
                 "This interpolation method is not supported for Timedelta Index yet."
             )
+
+    def test_interpolate_warn_index_not_sorted(self):
+        # GH 21037
+        ts = pd.Series(data=[10, 9, np.nan, 2, 1], index=[10, 9, 3, 2, 1])
+        with tm.assert_produces_warning(IndexNotSortedWarning):
+            ts.interpolate(method="index")
+        with tm.assert_produces_warning(IndexNotSortedWarning):
+            ts.interpolate(method="values")