diff --git a/airflow/www/templates/airflow/graph.html b/airflow/www/templates/airflow/graph.html
index 4866cdc357b56..892e2ee9f27ff 100644
--- a/airflow/www/templates/airflow/graph.html
+++ b/airflow/www/templates/airflow/graph.html
@@ -107,7 +107,7 @@
       <span class="loading-dot"></span>
     </span>
     <label class="switch-label">
-      <input class="switch-input" id="auto_refresh" type="checkbox" checked>
+      <input class="switch-input" id="auto_refresh" type="checkbox" {% if dag_run_state == 'running' %}checked{% endif %}>
       <span class="switch" aria-hidden="true"></span>
       Auto-refresh
     </label>
diff --git a/airflow/www/views.py b/airflow/www/views.py
index c5a3a5f7baa34..342add063c1a0 100644
--- a/airflow/www/views.py
+++ b/airflow/www/views.py
@@ -1842,7 +1842,8 @@ class GraphForm(DateTimeWithNumRunsWithDagRunsForm):
             nodes=nodes,
             edges=edges,
             show_external_log_redirect=task_log_reader.supports_external_link,
-            external_log_name=external_log_name)
+            external_log_name=external_log_name,
+            dag_run_state=dt_nr_dr_data['dr_state'])
 
     @expose('/duration')
     @has_dag_access(can_dag_read=True)