In header.php

  wp_nav_menu( array(
    'theme_location' => 'primary',
    'walker'  => new Child_Wrap()   
   ) );

Then in functions.php

class Child_Wrap extends Walker_Nav_Menu
{
    function start_lvl(&$output, $depth = 0, $args = array())
    {
        $indent = str_repeat("\t", $depth);
        $output .= "$indent<ul class=\"my-class\">\n";
    }

    function end_lvl(&$output, $depth = 0, $args = array())
    {
        $indent = str_repeat("\t", $depth);
        $output .= "$indent</ul>";
    }
}

This will replace the class “sub-menu” to “my-class”.