diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 12cb5f0ddd..de10c78d7b 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -2369,6 +2369,18 @@ def logp(self, value):
             alpha > 0,
             beta > 0)
 
+    def logcdf(self, value):
+        """
+        Compute the log CDF for the Gamma distribution
+        """
+        alpha = self.alpha
+        beta = self.beta
+        return bound(
+            tt.log(tt.gammainc(alpha, beta * value)),
+            value >= 0,
+            alpha > 0,
+            beta > 0)
+
     def _repr_latex_(self, name=None, dist=None):
         if dist is None:
             dist = self
diff --git a/pymc3/tests/test_distributions.py b/pymc3/tests/test_distributions.py
index 2fef74d2d2..e10a34c6d5 100644
--- a/pymc3/tests/test_distributions.py
+++ b/pymc3/tests/test_distributions.py
@@ -692,6 +692,10 @@ def test_fun(value, mu, sigma):
         self.pymc3_matches_scipy(
             Gamma, Rplus, {'mu': Rplusbig, 'sigma': Rplusbig}, test_fun)
 
+        self.check_logcdf(
+            Gamma, Rplus, {'alpha': Rplusbig, 'beta': Rplusbig},
+            lambda value, alpha, beta: sp.gamma.logcdf(value, alpha, scale=1.0/beta))
+
     def test_inverse_gamma(self):
         self.pymc3_matches_scipy(
             InverseGamma, Rplus, {'alpha': Rplus, 'beta': Rplus},