diff --git a/readthedocs/projects/tasks.py b/readthedocs/projects/tasks.py
index c91c7598ca7..5ee85ef8fc5 100644
--- a/readthedocs/projects/tasks.py
+++ b/readthedocs/projects/tasks.py
@@ -404,6 +404,15 @@ def run(self, version_pk):  # pylint: disable=arguments-differ
     default_retry_delay=7 * 60,
 )
 def update_docs_task(self, version_pk, *args, **kwargs):
+    import signal
+
+    def sigterm_received(*args, **kwargs):
+        log.warning('SIGTERM received. Waiting for build to stop gracefully after it finishes.')
+
+    # Do not send the SIGTERM signal to childs (pip is automatically killed when
+    # receives SIGTERM and make the build to fail one command and stop build)
+    signal.signal(signal.SIGTERM, sigterm_received)
+
     try:
         step = UpdateDocsTaskStep(task=self)
         return step.run(version_pk, *args, **kwargs)