diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 4d6bf2a0507..532074ba41f 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -23,6 +23,7 @@ Enhancements
   thread lock by default for reading from netCDF files. This avoids possible
   segmentation faults for reading from netCDF4 files when HDF5 is not
   configured properly for concurrent access (:issue:`444`).
+- Added support for serializing arrays of complex numbers with `engine='h5netcdf'`.
 - The new :py:func:`~xray.save_mfdataset` function allows for saving multiple
   datasets to disk simultaneously. This is useful when processing large datasets
   with dask.array. For example, to save a dataset too big to fit into memory
diff --git a/xray/backends/netCDF4_.py b/xray/backends/netCDF4_.py
index 7fb61f38cd7..4cdb65c2fb6 100644
--- a/xray/backends/netCDF4_.py
+++ b/xray/backends/netCDF4_.py
@@ -57,12 +57,14 @@ def _nc4_values_and_dtype(var):
         if len(var) > 0:
             var = var.astype('O')
         dtype = str
-    elif var.dtype.kind in ['i', 'u', 'f', 'S']:
+    elif var.dtype.kind == 'S':
         # use character arrays instead of unicode, because unicode suppot in
         # netCDF4 is still rather buggy
         data, dims = maybe_convert_to_char_array(var.data, var.dims)
         var = Variable(dims, data, var.attrs, var.encoding)
         dtype = var.dtype
+    elif var.dtype.kind in ['i', 'u', 'f', 'c']:
+        dtype = var.dtype
     else:
         raise ValueError('cannot infer dtype for netCDF4 variable')
     return var, dtype
diff --git a/xray/test/test_backends.py b/xray/test/test_backends.py
index 0dbfb0d7c00..5288d86dc90 100644
--- a/xray/test/test_backends.py
+++ b/xray/test/test_backends.py
@@ -699,6 +699,11 @@ def test_orthogonal_indexing(self):
         # doesn't work for h5py (without using dask as an intermediate layer)
         pass
 
+    def test_complex(self):
+        expected = Dataset({'x': ('y', np.ones(5) + 1j * np.ones(5))})
+        with self.roundtrip(expected) as actual:
+            self.assertDatasetEqual(expected, actual)
+
 
 @requires_dask
 @requires_netCDF4