diff --git a/doc/source/whatsnew/v0.19.0.txt b/doc/source/whatsnew/v0.19.0.txt
index 4cc16aac15f8b..022d8545ca658 100644
--- a/doc/source/whatsnew/v0.19.0.txt
+++ b/doc/source/whatsnew/v0.19.0.txt
@@ -549,3 +549,5 @@ Bug Fixes
 - Bug in ``groupby`` with ``as_index=False`` returns all NaN's when grouping on multiple columns including a categorical one (:issue:`13204`)
 
 - Bug where ``pd.read_gbq()`` could throw ``ImportError: No module named discovery`` as a result of a naming conflict with another python package called apiclient  (:issue:`13454`)
+
+- Bug when calling ``Series.argmax`` with infinite values (:issue:`13595`)
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index f390e3f04a6c3..7c13c23f731da 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -454,8 +454,7 @@ def nanargmax(values, axis=None, skipna=True):
     """
     Returns -1 in the NA case
     """
-    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='-inf',
-                                         isfinite=True)
+    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='-inf')
     result = values.argmax(axis)
     result = _maybe_arg_null_out(result, axis, mask, skipna)
     return result
@@ -465,8 +464,7 @@ def nanargmin(values, axis=None, skipna=True):
     """
     Returns -1 in the NA case
     """
-    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='+inf',
-                                         isfinite=True)
+    values, mask, dtype, _ = _get_values(values, skipna, fill_value_typ='+inf')
     result = values.argmin(axis)
     result = _maybe_arg_null_out(result, axis, mask, skipna)
     return result
diff --git a/pandas/tests/series/test_analytics.py b/pandas/tests/series/test_analytics.py
index d9e2d8096c8d7..03c34b90c7a6c 100644
--- a/pandas/tests/series/test_analytics.py
+++ b/pandas/tests/series/test_analytics.py
@@ -1282,6 +1282,14 @@ def test_idxmax(self):
         result = s.idxmin()
         self.assertEqual(result, 1.1)
 
+        # Infinite values
+        # GH 13595
+        s = pd.Series([1, 2, np.inf])
+        result = s.idxmax()
+        self.assertEqual(result, 2)
+        result = s.idxmax(skipna=False)
+        self.assertEqual(result, 2)
+
     def test_numpy_argmax(self):
 
         # argmax is aliased to idxmax
diff --git a/pandas/tests/test_nanops.py b/pandas/tests/test_nanops.py
index 904bedde03312..0c85ec9638ca9 100644
--- a/pandas/tests/test_nanops.py
+++ b/pandas/tests/test_nanops.py
@@ -41,6 +41,7 @@ def setUp(self):
 
         self.arr_inf = self.arr_float * np.inf
         self.arr_float_inf = np.vstack([self.arr_float, self.arr_inf])
+        self.arr_float_neg_inf = -1 * self.arr_float_inf
         self.arr_float1_inf = np.vstack([self.arr_float1, self.arr_inf])
         self.arr_inf_float1 = np.vstack([self.arr_inf, self.arr_float1])
         self.arr_inf_inf = np.vstack([self.arr_inf, self.arr_inf])
@@ -234,7 +235,7 @@ def check_fun(self, testfunc, targfunc, testar, targar=None,
 
     def check_funs(self, testfunc, targfunc, allow_complex=True,
                    allow_all_nan=True, allow_str=True, allow_date=True,
-                   allow_tdelta=True, allow_obj=True, **kwargs):
+                   allow_tdelta=True, allow_obj=True, allow_inf=True, **kwargs):
         self.check_fun(testfunc, targfunc, 'arr_float', **kwargs)
         self.check_fun(testfunc, targfunc, 'arr_float_nan', 'arr_float',
                        **kwargs)
@@ -287,6 +288,10 @@ def check_funs(self, testfunc, targfunc, allow_complex=True,
                                    allow_complex=allow_complex)
             self.check_fun(testfunc, targfunc, 'arr_obj', **kwargs)
 
+        if allow_inf:
+            self.check_fun(testfunc, targfunc, 'arr_float_inf', **kwargs)
+            self.check_fun(testfunc, targfunc, 'arr_float_neg_inf', **kwargs)
+
     def check_funs_ddof(self,
                         testfunc,
                         targfunc,
@@ -295,7 +300,7 @@ def check_funs_ddof(self,
                         allow_str=True,
                         allow_date=False,
                         allow_tdelta=False,
-                        allow_obj=True, ):
+                        allow_obj=True):
         for ddof in range(3):
             try:
                 self.check_funs(testfunc, targfunc, allow_complex,