diff --git a/doc/source/whatsnew/v0.20.2.txt b/doc/source/whatsnew/v0.20.2.txt
index 13365401f1d1c..8182a1c111a0a 100644
--- a/doc/source/whatsnew/v0.20.2.txt
+++ b/doc/source/whatsnew/v0.20.2.txt
@@ -80,6 +80,7 @@ Groupby/Resample/Rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
 
 - Bug creating datetime rolling window on an empty DataFrame (:issue:`15819`)
+- Bug in ``rolling.cov()`` with offset window (:issue:`16058`)
 
 
 Sparse
diff --git a/pandas/core/window.py b/pandas/core/window.py
index cf1bad706ae1d..ba7e79944ab0e 100644
--- a/pandas/core/window.py
+++ b/pandas/core/window.py
@@ -81,6 +81,7 @@ def __init__(self, obj, window=None, min_periods=None, freq=None,
         self.freq = freq
         self.center = center
         self.win_type = win_type
+        self.win_freq = None
         self.axis = obj._get_axis_number(axis) if axis is not None else None
         self.validate()
 
@@ -996,7 +997,12 @@ def cov(self, other=None, pairwise=None, ddof=1, **kwargs):
             # only default unset
             pairwise = True if pairwise is None else pairwise
         other = self._shallow_copy(other)
-        window = self._get_window(other)
+
+        # GH 16058: offset window
+        if self.is_freq_type:
+            window = self.win_freq
+        else:
+            window = self._get_window(other)
 
         def _get_cov(X, Y):
             # GH #12373 : rolling functions error on float32 data
@@ -1088,6 +1094,7 @@ def validate(self):
                                           "based windows")
 
             # this will raise ValueError on non-fixed freqs
+            self.win_freq = self.window
             self.window = freq.nanos
             self.win_type = 'freq'
 
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index 6a640d62108b3..cbb3c345a9353 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -3833,3 +3833,26 @@ def test_non_monotonic(self):
         df2 = df.sort_values('B')
         result = df2.groupby('A').rolling('4s', on='B').C.mean()
         tm.assert_series_equal(result, expected)
+
+    def test_rolling_cov_offset(self):
+        # GH16058
+
+        idx = pd.date_range('2017-01-01', periods=24, freq='1h')
+        ss = pd.Series(np.arange(len(idx)), index=idx)
+
+        result = ss.rolling('2h').cov()
+        expected = pd.Series([np.nan] + [0.5 for _ in range(len(idx) - 1)],
+                             index=idx)
+        tm.assert_series_equal(result, expected)
+
+        expected2 = ss.rolling(2, min_periods=1).cov()
+        tm.assert_series_equal(result, expected2)
+
+        result = ss.rolling('3h').cov()
+        expected = pd.Series([np.nan, 0.5] +
+                             [1.0 for _ in range(len(idx) - 2)],
+                             index=idx)
+        tm.assert_series_equal(result, expected)
+
+        expected2 = ss.rolling(3, min_periods=1).cov()
+        tm.assert_series_equal(result, expected2)