diff --git a/src/core/ad.jl b/src/core/ad.jl
index 1d466f93b..5fa0dec1c 100644
--- a/src/core/ad.jl
+++ b/src/core/ad.jl
@@ -125,3 +125,11 @@ Tracker.@grad function binomlogpdf(n::Int, p::Tracker.TrackedReal, x::Int)
     return binomlogpdf(n, Tracker.data(p), x),
         Δ->(nothing, Δ * (x / p - (n - x) / (1 - p)), nothing)
 end
+
+
+import StatsFuns: poislogpdf
+poislogpdf(v::Tracker.TrackedReal, x::Int) = Tracker.track(poislogpdf, v, x)
+Tracker.@grad function poislogpdf(v::Tracker.TrackedReal, x::Int)
+      return poislogpdf(Tracker.data(v), x),
+          Δ->(Δ * (x/v - 1), nothing)
+end
diff --git a/test/ad.jl/AD_compatibility_with_distributions.jl b/test/ad.jl/AD_compatibility_with_distributions.jl
index 7ef15d54e..d65a5b985 100644
--- a/test/ad.jl/AD_compatibility_with_distributions.jl
+++ b/test/ad.jl/AD_compatibility_with_distributions.jl
@@ -46,3 +46,21 @@ let
         atol=1e-8,
     )
 end
+
+let
+    foo = p->poislogpdf(1, p)
+    @test isapprox(
+        Tracker.gradient(foo, 0.5)[1],
+        central_fdm(5, 1)(foo, 0.5);
+        rtol=1e-8,
+        atol=1e-8,
+    )
+
+    bar = p->logpdf(Poisson(1), 3)
+    @test isapprox(
+        Tracker.gradient(bar, 0.5)[1],
+        central_fdm(5, 1)(bar, 0.5);
+        rtol=1e-8,
+        atol=1e-8,
+    )
+end