Just add this jQuery library in the header of your page.
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.0/jquery.min.js"></script>
Add this JavaScript code in the footer of your page.
<script type="text/javascript">
jQuery(".my_menu li").click(function (e) {
jQuery(this).addClass("my_current_page_item").siblings().removeClass("my_current_page_item");
});
</script>
This is the HTML code.
<div class="my_menu">
<ul>
<li class="page_item">Item 01</li>
<li class="page_item">Item 02</li>
<li class="page_item">Item 03</li>
<li class="page_item">Item 04</li>
<li class="page_item">Item 05</li>
</ul>
</div>
Example:
