Wordpress: How can I add url GET parameter to my main menu items

The filter hook wp_get_nav_menu_items is used to manipulate the Nav Menus. The post_title used in the example is the title of the Menu (Navigation Label), not of the post/page.

Drop this code in your functions.php file, adjust the post_title and ?my_var=test to your needs. Note that better than functions is to create your own plugin.

add_filter( 'wp_get_nav_menu_items','nav_items', 11, 3 );

function nav_items( $items, $menu, $args ) 
{
    if( is_admin() )
        return $items;

    foreach( $items as $item ) 
    {
        if( 'Home' == $item->post_title)
            $item->url .= '?my_var=test';

    }
    return $items;
}