diff --git a/docs/source/_static/custom.css b/docs/source/_static/custom.css
new file mode 100644
index 000000000..dfabf9c40
--- /dev/null
+++ b/docs/source/_static/custom.css
@@ -0,0 +1,6 @@
+/* Fix version switcher dropdown overflow - GitHub issue #578 */
+.version-switcher__menu {
+    max-height: 60vh;
+    overflow-y: auto !important;
+    overflow-x: hidden;
+}
diff --git a/docs/source/conf.py b/docs/source/conf.py
index 4695b6872..3a08becf3 100644
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -46,5 +46,6 @@
     ],
 }
 html_static_path = ["_static"]
+html_css_files = ["custom.css"]
 html_logo = "_static/logo.svg"
 html_favicon = "_static/favicon.ico"