diff --git a/lib/iris/quickplot.py b/lib/iris/quickplot.py
index 032fee557c..aab4226661 100644
--- a/lib/iris/quickplot.py
+++ b/lib/iris/quickplot.py
@@ -100,8 +100,10 @@ def _label_with_points(cube, result=None, ndims=2, coords=None):
 def _get_titles(u_object, v_object):
     if u_object is None:
         u_object = iplt._u_object_from_v_object(v_object)
-    xlabel = _title(u_object, with_units=True)
-    ylabel = _title(v_object, with_units=True)
+    xunits = u_object is not None and not u_object.units.is_time_reference()
+    yunits = not v_object.units.is_time_reference()
+    xlabel = _title(u_object, with_units=xunits)
+    ylabel = _title(v_object, with_units=yunits)
     title = ''
     if u_object is None:
         title = _title(v_object, with_units=False)
diff --git a/lib/iris/tests/results/visual_tests/test_quickplot.TestTimeReferenceUnitsLabels.test_not_reference_time_units.0.png b/lib/iris/tests/results/visual_tests/test_quickplot.TestTimeReferenceUnitsLabels.test_not_reference_time_units.0.png
new file mode 100644
index 0000000000..dd784e2ffc
Binary files /dev/null and b/lib/iris/tests/results/visual_tests/test_quickplot.TestTimeReferenceUnitsLabels.test_not_reference_time_units.0.png differ
diff --git a/lib/iris/tests/results/visual_tests/test_quickplot.TestTimeReferenceUnitsLabels.test_reference_time_units.0.png b/lib/iris/tests/results/visual_tests/test_quickplot.TestTimeReferenceUnitsLabels.test_reference_time_units.0.png
new file mode 100644
index 0000000000..f0a64ae9a7
Binary files /dev/null and b/lib/iris/tests/results/visual_tests/test_quickplot.TestTimeReferenceUnitsLabels.test_reference_time_units.0.png differ
diff --git a/lib/iris/tests/test_quickplot.py b/lib/iris/tests/test_quickplot.py
index 2593673c64..065c705e8b 100644
--- a/lib/iris/tests/test_quickplot.py
+++ b/lib/iris/tests/test_quickplot.py
@@ -21,6 +21,8 @@
 # import iris tests first so that some things can be initialised before importing anything else
 import iris.tests as tests
 
+import matplotlib.pyplot as plt
+
 import iris
 import iris.plot as iplt
 import iris.quickplot as qplt
@@ -172,5 +174,24 @@ def test_alignment(self):
         self.check_graphic()
 
 
+@tests.skip_data
+class TestTimeReferenceUnitsLabels(tests.GraphicsTest):
+
+    def setUp(self):
+        path = tests.get_data_path(('PP', 'aPProt1', 'rotatedMHtimecube.pp'))
+        self.cube = iris.load_cube(path)[:, 0, 0]
+
+    def test_reference_time_units(self):
+        # units should not be displayed for a reference time
+        qplt.plot(self.cube.coord('time'), self.cube)
+        plt.gcf().autofmt_xdate()
+        self.check_graphic()
+
+    def test_not_reference_time_units(self):
+        # units should be displayed for other time coordinates
+        qplt.plot(self.cube.coord('forecast_period'), self.cube)
+        self.check_graphic()
+
+
 if __name__ == "__main__":
     tests.main()