diff --git a/pymc/distributions/continuous.py b/pymc/distributions/continuous.py
index 76932db6f6..b8857b2fe2 100644
--- a/pymc/distributions/continuous.py
+++ b/pymc/distributions/continuous.py
@@ -1641,7 +1641,22 @@ def logp(value, b, kappa, mu):
             kappa > 0,
             msg="b > 0, kappa > 0",
         )
-
+    def icdf(value, b, kappa, mu):
+        res = pt.switch(pt.le(b, 0), 
+                        lambda: ValueError("Scale Parameter b must be positive"),
+                        pt.switch(
+                            pt.le(value, 0.5),
+                            lambda: mu - (b / kappa) * pt.log(2 * value),
+                            lambda: mu + (b / kappa) * pt.log(2 * (1 - value))
+                        )
+                       )
+        res = check_icdf_parameters(res, value)
+        return check_icdf_parameters(
+            res,
+            b > 0,
+            kappa > 0,
+            msg="b > 0, kappa > 0"
+        )
 
 class LogNormal(PositiveContinuous):
     r"""
diff --git a/tests/distributions/test_continuous.py b/tests/distributions/test_continuous.py
index 80bbb816c8..f2041ed22d 100644
--- a/tests/distributions/test_continuous.py
+++ b/tests/distributions/test_continuous.py
@@ -488,6 +488,11 @@ def test_laplace_asymmetric(self):
             laplace_asymmetric_logpdf,
             decimal=select_by_precision(float64=6, float32=2),
         )
+        check_icdf(
+            pm.AsymmetricLaplace,
+            {"b": Rplus, "kappa": Rplus, "mu": R},
+            lambda q, kappa, mu, b: st.laplace_asymmetric.ppf(q, kappa, mu, b)
+        )
 
     def test_lognormal(self):
         check_logp(