How to place a div center of the window after scrolling

I suggest the following solution:

1) In JS when you want to show a window:

{
var width = $(window).width();
var heigth = $(window).height();
var myWindow = $('.my-window');
    myWindow .show('fast');
    myWindow .offset(
    {
        left: (width - myWindow .width()) / 2 + $(window).scrollLeft(),
        top: (heigth - myWindow .height()) / 2 + $(window).scrollTop()
    });
}

2) in CSS: .my-window

{
    position: fixed;