diff --git a/python/ray/tune/tests/test_api.py b/python/ray/tune/tests/test_api.py
index de2977210..d16a512f7 100644
--- a/python/ray/tune/tests/test_api.py
+++ b/python/ray/tune/tests/test_api.py
@@ -2,6 +2,7 @@ from collections import Counter
 import shutil
 import tempfile
 import copy
+import numpy as np
 import os
 import time
 import unittest
@@ -1019,6 +1020,23 @@ class TrainableFunctionApiTest(unittest.TestCase):
         diff = time.time() - start
         self.assertLess(diff, 9)
 
+    def testInfiniteTrials(self):
+        def train(config):
+            time.sleep(0.5)
+            tune.report(np.random.uniform(-10., 10.))
+
+        start = time.time()
+        out = tune.run(train, num_samples=-1, time_budget_s=10)
+        taken = time.time() - start
+
+        # Allow for init time overhead
+        self.assertLessEqual(taken, 20.)
+        self.assertGreaterEqual(len(out.trials), 0)
+
+        status = dict(Counter([trial.status for trial in out.trials]))
+        self.assertGreaterEqual(status["TERMINATED"], 1)
+        self.assertLessEqual(status.get("PENDING", 0), 1)
+
     def testMetricCheckingEndToEnd(self):
         from ray import tune