diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 982331b4ea45..b4fadf0ed35a 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -5820,9 +5820,13 @@ def _pcolorargs(self, funcname, *args, shading='auto', **kwargs):
                                 f" see help({funcname})")
         else:    # ['nearest', 'gouraud']:
             if (Nx, Ny) != (ncols, nrows):
-                raise TypeError('Dimensions of C %s are incompatible with'
-                                ' X (%d) and/or Y (%d); see help(%s)' % (
-                                    C.shape, Nx, Ny, funcname))
+                if (Nx, Ny) == (ncols + 1, nrows + 1):
+                    X = (X[1:, 1:] + X[:1, :-1]) / 2
+                    Y = (Y[1:, :-1] + Y[:-1, :-1]) / 2
+                else:
+                    raise TypeError('Dimensions of C %s are incompatible with'
+                                    ' X (%d) and/or Y (%d); see help(%s)' % (
+                                        C.shape, Nx, Ny, funcname))
             if shading == 'nearest':
                 # grid is specified at the center, so define corners
                 # at the midpoints between the grid centers and then use the
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 947c706e900f..bf77a3abf63d 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -1399,6 +1399,19 @@ def test_pcolormesh_alpha():
     ax4.pcolormesh(Qx, Qy, Z, cmap=cmap, shading='gouraud', zorder=1)
 
 
+@check_figures_equal()
+def test_pcolormesh_gouraud(fig_test, fig_ref):
+    ax_test = fig_test.subplots()
+    ax_ref = fig_ref.subplots()
+    x = np.arange(-4, 5)
+    y = np.arange(-6, 7)
+    xe = np.linspace(-4.5, 4.5, 10)
+    ye = np.linspace(-6.5, 6.5, 14)
+    c = np.exp(-0.5*0.125*(x.reshape(1, -1)**2 + y.reshape(-1, 1)**2))
+    ax_ref.pcolormesh(x, y, c, shading='gouraud')
+    ax_test.pcolormesh(xe, ye, c, shading='gouraud')
+
+
 @pytest.mark.parametrize("dims,alpha", [(3, 1), (4, 0.5)])
 @check_figures_equal(extensions=["png"])
 def test_pcolormesh_rgba(fig_test, fig_ref, dims, alpha):
@@ -1476,9 +1489,13 @@ def test_pcolorargs():
     with pytest.raises(TypeError):
         ax.pcolormesh(X, Y, Z.T)
     with pytest.raises(TypeError):
-        ax.pcolormesh(x, y, Z[:-1, :-1], shading="gouraud")
+        ax.pcolormesh(x, y, Z[:-2, :-2], shading="gouraud")
+    with pytest.raises(TypeError):
+        ax.pcolormesh(X, Y, Z[:-2, :-2], shading="gouraud")
+    with pytest.raises(TypeError):
+        ax.pcolormesh(x[1:], y[1:], Z, shading="gouraud")
     with pytest.raises(TypeError):
-        ax.pcolormesh(X, Y, Z[:-1, :-1], shading="gouraud")
+        ax.pcolormesh(X[1:, 1:], Y[1:, 1:], Z, shading="gouraud")
     x[0] = np.NaN
     with pytest.raises(ValueError):
         ax.pcolormesh(x, y, Z[:-1, :-1])