diff --git a/compose/cli/main.py b/compose/cli/main.py
index 6f8cc47c8..4319d0ada 100644
--- a/compose/cli/main.py
+++ b/compose/cli/main.py
@@ -1256,6 +1256,7 @@ def run_one_off_container(container_options, project, service, options, project_
     use_cli = not environment.get_boolean('COMPOSE_INTERACTIVE_NO_CLI')
 
     signals.set_signal_handler_to_shutdown()
+    signals.set_signal_handler_to_hang_up()
     try:
         try:
             if IS_WINDOWS_PLATFORM or use_cli:
@@ -1273,10 +1274,10 @@ def run_one_off_container(container_options, project, service, options, project_
                 service.start_container(container)
                 pty.start(sockets)
                 exit_code = container.wait()
-        except signals.ShutdownException:
+        except (signals.ShutdownException):
             project.client.stop(container.id)
             exit_code = 1
-    except signals.ShutdownException:
+    except (signals.ShutdownException, signals.HangUpException):
         project.client.kill(container.id)
         remove_container(force=True)
         sys.exit(2)
diff --git a/compose/cli/signals.py b/compose/cli/signals.py
index 9b360c44e..44def2ece 100644
--- a/compose/cli/signals.py
+++ b/compose/cli/signals.py
@@ -10,6 +10,10 @@ class ShutdownException(Exception):
     pass
 
 
+class HangUpException(Exception):
+    pass
+
+
 def shutdown(signal, frame):
     raise ShutdownException()
 
@@ -23,6 +27,16 @@ def set_signal_handler_to_shutdown():
     set_signal_handler(shutdown)
 
 
+def hang_up(signal, frame):
+    raise HangUpException()
+
+
+def set_signal_handler_to_hang_up():
+    # on Windows a ValueError will be raised if trying to set signal handler for SIGHUP
+    if not IS_WINDOWS_PLATFORM:
+        signal.signal(signal.SIGHUP, hang_up)
+
+
 def ignore_sigpipe():
     # Restore default behavior for SIGPIPE instead of raising
     # an exception when encountered.
diff --git a/tests/acceptance/cli_test.py b/tests/acceptance/cli_test.py
index 8fb6dffec..9dd03b72f 100644
--- a/tests/acceptance/cli_test.py
+++ b/tests/acceptance/cli_test.py
@@ -1876,6 +1876,19 @@ class CLITestCase(DockerClientTestCase):
             'simplecomposefile_simple_run_1',
             'exited'))
 
+    def test_run_handles_sighup(self):
+        proc = start_process(self.base_dir, ['run', '-T', 'simple', 'top'])
+        wait_on_condition(ContainerStateCondition(
+            self.project.client,
+            'simplecomposefile_simple_run_1',
+            'running'))
+
+        os.kill(proc.pid, signal.SIGHUP)
+        wait_on_condition(ContainerStateCondition(
+            self.project.client,
+            'simplecomposefile_simple_run_1',
+            'exited'))
+
     @mock.patch.dict(os.environ)
     def test_run_unicode_env_values_from_system(self):
         value = 'ą, ć, ę, ł, ń, ó, ś, ź, ż'