diff --git a/python/ray/log_monitor.py b/python/ray/log_monitor.py
index 6d534ff50..a8fce2fb1 100644
--- a/python/ray/log_monitor.py
+++ b/python/ray/log_monitor.py
@@ -8,6 +8,7 @@ import glob
 import json
 import logging
 import os
+import shutil
 import time
 import traceback
 
@@ -85,7 +86,26 @@ class LogMonitor(object):
             file_info = self.open_file_infos.pop(0)
             file_info.file_handle.close()
             file_info.file_handle = None
-            self.closed_file_infos.append(file_info)
+            try:
+                # Test if the worker process that generated the log file
+                # is still alive.
+                os.kill(file_info.worker_pid, 0)
+            except OSError:
+                # The process is not alive any more, so move the log file
+                # out of the log directory so glob.glob will not be slowed
+                # by it.
+                target = os.path.join(self.logs_dir, "old",
+                                      os.path.basename(file_info.filename))
+                try:
+                    shutil.move(file_info.filename, target)
+                except (IOError, OSError) as e:
+                    if e.errno == errno.ENOENT:
+                        logger.warning("Warning: The file {} was not "
+                                       "found.".format(file_info.filename))
+                    else:
+                        raise e
+            else:
+                self.closed_file_infos.append(file_info)
         self.can_open_more_files = True
 
     def update_log_filenames(self):
diff --git a/python/ray/node.py b/python/ray/node.py
index c80a4fd6b..5f09046e9 100644
--- a/python/ray/node.py
+++ b/python/ray/node.py
@@ -180,6 +180,8 @@ class Node(object):
         # Create a directory to be used for process log files.
         self._logs_dir = os.path.join(self._session_dir, "logs")
         try_to_create_directory(self._logs_dir, warn_if_exist=False)
+        old_logs_dir = os.path.join(self._logs_dir, "old")
+        try_to_create_directory(old_logs_dir, warn_if_exist=False)
 
     def get_resource_spec(self):
         """Resolve and return the current resource spec for the node."""
diff --git a/python/ray/tests/test_basic.py b/python/ray/tests/test_basic.py
index 3b575c1e0..28f3cea75 100644
--- a/python/ray/tests/test_basic.py
+++ b/python/ray/tests/test_basic.py
@@ -28,6 +28,7 @@ import pickle
 import pytest
 
 import ray
+import ray.ray_constants as ray_constants
 import ray.tests.cluster_utils
 import ray.tests.utils
 
@@ -3140,3 +3141,38 @@ def test_invalid_unicode_in_worker_log(shutdown_only):
 
     # Make sure that nothing has died.
     assert ray.services.remaining_processes_alive()
+
+
+@pytest.mark.skip(reason="This test is too expensive to run.")
+def test_move_log_files_to_old(shutdown_only):
+    info = ray.init(num_cpus=1)
+
+    logs_dir = os.path.join(info["session_dir"], "logs")
+
+    @ray.remote
+    class Actor(object):
+        def f(self):
+            print("function f finished")
+
+    # First create a temporary actor.
+    actors = [
+        Actor.remote() for i in range(ray_constants.LOG_MONITOR_MAX_OPEN_FILES)
+    ]
+    ray.get([a.f.remote() for a in actors])
+
+    # Make sure no log files are in the "old" directory before the actors
+    # are killed.
+    assert len(glob.glob("{}/old/worker*.out".format(logs_dir))) == 0
+
+    # Now kill the actors so the files get moved to logs/old/.
+    [a.__ray_terminate__.remote() for a in actors]
+
+    while True:
+        log_file_paths = glob.glob("{}/old/worker*.out".format(logs_dir))
+        if len(log_file_paths) > 0:
+            with open(log_file_paths[0], "r") as f:
+                assert "function f finished\n" in f.readlines()
+            break
+
+    # Make sure that nothing has died.
+    assert ray.services.remaining_processes_alive()