Simple Maintenance plugin can be easily installed to show a maintenance mode page. It allows you to maintain your site on the back end by displaying a temporary maintenance page on the front end.
The plugin does not require any additional configuration or setup. All you need to do is activate it and maintenance mode will be automatically enabled. It is very lightweight yet powerful. It uses the HTML5 layout which makes the maintenance mode page viewable from a mobile device.
For more information please check the WordPress Maintenance Mode Plugin documentation page