diff --git a/numpyro/distributions/kl.py b/numpyro/distributions/kl.py
index 2fcfecb2f..3d79dca01 100644
--- a/numpyro/distributions/kl.py
+++ b/numpyro/distributions/kl.py
@@ -85,12 +85,12 @@ def kl_divergence(p, q):
 
 @dispatch(Delta, Distribution)
 def kl_divergence(p, q):
-    return -q.log_prob(p.v)
+    return -q.log_prob(p.v) + p.log_density
 
 
 @dispatch(Delta, ExpandedDistribution)
 def kl_divergence(p, q):
-    return -q.log_prob(p.v)
+    return -q.log_prob(p.v) + p.log_density
 
 
 @dispatch(Independent, Independent)
diff --git a/test/test_distributions.py b/test/test_distributions.py
index dbcb21218..0362adf28 100644
--- a/test/test_distributions.py
+++ b/test/test_distributions.py
@@ -2814,6 +2814,15 @@ def test_kl_delta_normal_shape(batch_shape):
     assert kl_divergence(p, q).shape == batch_shape
 
 
+def test_kl_delta_normal():
+    v = np.random.normal()
+    loc = np.random.normal()
+    scale = np.exp(np.random.normal())
+    p = dist.Delta(v, 10.0)
+    q = dist.Normal(loc, scale)
+    assert_allclose(kl_divergence(p, q), 10.0 - q.log_prob(v))
+
+
 @pytest.mark.parametrize("batch_shape", [(), (4,), (2, 3)], ids=str)
 @pytest.mark.parametrize("event_shape", [(), (4,), (2, 3)], ids=str)
 def test_kl_independent_normal(batch_shape, event_shape):