diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index b28beb9e3b2..87b019b54aa 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -47,6 +47,9 @@ Bug fixes
 - Fixed labeled indexing with slice bounds given by xarray objects with
   datetime64 or timedelta64 dtypes (:issue:`1240`).
   By `Stephan Hoyer <https://github.com/shoyer>`_.
+- Fixed a bug in decode_cf_datetime where ``int32`` arrays weren't parsed
+  correctly (:issue:`2002`).
+  By `Fabien Maussion <https://github.com/fmaussion>`_.
 
 .. _whats-new.0.10.2:
 
diff --git a/xarray/coding/times.py b/xarray/coding/times.py
index 1bb4e31ae7e..8a1e9f82c6c 100644
--- a/xarray/coding/times.py
+++ b/xarray/coding/times.py
@@ -166,7 +166,8 @@ def decode_cf_datetime(num_dates, units, calendar=None):
 
         # Cast input dates to integers of nanoseconds because `pd.to_datetime`
         # works much faster when dealing with integers
-        flat_num_dates_ns_int = (flat_num_dates *
+        # make _NS_PER_TIME_DELTA an array to ensure type upcasting
+        flat_num_dates_ns_int = (flat_num_dates.astype(np.float64) *
                                  _NS_PER_TIME_DELTA[delta]).astype(np.int64)
 
         dates = (pd.to_timedelta(flat_num_dates_ns_int, 'ns') +
diff --git a/xarray/tests/test_coding_times.py b/xarray/tests/test_coding_times.py
index b85f92ece66..ab33329b51a 100644
--- a/xarray/tests/test_coding_times.py
+++ b/xarray/tests/test_coding_times.py
@@ -49,6 +49,7 @@ def test_cf_datetime(self):
             ([0.5, 1.5], 'hours since 1900-01-01T00:00:00'),
             (0, 'milliseconds since 2000-01-01T00:00:00'),
             (0, 'microseconds since 2000-01-01T00:00:00'),
+            (np.int32(788961600), 'seconds since 1981-01-01'),  # GH2002
         ]:
             for calendar in ['standard', 'gregorian', 'proleptic_gregorian']:
                 expected = _ensure_naive_tz(