How to change active class while click to another link in bootstrap use jquery?

You are binding you click on the wrong element, you should bind it to the a.

You are prevent default event to occur on the li, but li have no default behavior, a does.

Try this:

$(document).ready(function () {
    $('.nav li a').click(function(e) {

        $('.nav li.active').removeClass('active');

        var $parent = $(this).parent();
        $parent.addClass('active');
        e.preventDefault();
    });
});