diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index f6e92b70c6ac..69e056140ea0 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -1565,6 +1565,17 @@ def test_hist_step_log_bottom():
     ax.set_ylim(9e-3, 1e3)
 
 
+def test_hist_unequal_bins_density():
+    # Test correct behavior of normalized histogram with unequal bins
+    # https://github.com/matplotlib/matplotlib/issues/9557
+    rng = np.random.RandomState(57483)
+    t = rng.randn(100)
+    bins = [-3, -1, -0.5, 0, 1, 5]
+    mpl_heights, _, _ = plt.hist(t, bins=bins, density=True)
+    np_heights, _ = np.histogram(t, bins=bins, density=True)
+    assert_allclose(mpl_heights, np_heights)
+
+
 def contour_dat():
     x = np.linspace(-3, 5, 150)
     y = np.linspace(-3, 5, 120)