diff --git a/xarray/plot/utils.py b/xarray/plot/utils.py
index 177c2de7041..7f417648604 100644
--- a/xarray/plot/utils.py
+++ b/xarray/plot/utils.py
@@ -297,6 +297,10 @@ def _determine_cmap_params(
                 levels = ticker.tick_values(vmin, vmax)
         vmin, vmax = levels[0], levels[-1]
 
+        # GH10911
+        if calc_data.max() >= levels[-1]:
+            levels[-1] = np.nextafter(levels[-1], np.inf)
+
     # GH3734
     if vmin == vmax:
         vmin, vmax = mpl.ticker.LinearLocator(2).tick_values(vmin, vmax)
diff --git a/xarray/tests/test_plot.py b/xarray/tests/test_plot.py
index 40f950d246d..3d6706545d4 100644
--- a/xarray/tests/test_plot.py
+++ b/xarray/tests/test_plot.py
@@ -1209,8 +1209,8 @@ def test_discrete_colormap_list_of_levels(self) -> None:
         ]:
             for kind in ["imshow", "pcolormesh", "contourf", "contour"]:
                 primitive = getattr(self.darray.plot, kind)(levels=levels)
-                assert_array_equal(levels, primitive.norm.boundaries)
-                assert max(levels) == primitive.norm.vmax
+                np.testing.assert_array_almost_equal(levels, primitive.norm.boundaries)
+                assert max(levels) <= primitive.norm.vmax
                 assert min(levels) == primitive.norm.vmin
                 if kind != "contour":
                     assert extend == primitive.cmap.colorbar_extend