WP Nav Menu - custom wordpress menu HTML structure

Try with below code

wp_nav_menu(
 array (
    'menu'            => 'main-menu',
    'container'       => '',// or false
    'container_id'    => FALSE,
    'menu_class'      => '',
    'menu_id'         => FALSE,
    'items_wrap'    => '%3$s',
    'depth'           => 1,
    'walker'          => new Description_Walker
 )
);

Put below code in your active functions.php

class Description_Walker extends Walker_Nav_Menu
{
    /**
     * Start the element output.
     *
     * @param  string $output Passed by reference. Used to append additional content.
     * @param  object $item   Menu item data object.
     * @param  int $depth     Depth of menu item. May be used for padding.
     * @param  array|object $args    Additional strings. Actually always an 
     * @return void
     */
    function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 )
    {
        $classes     = empty ( $item->classes ) ? array () : (array) $item->classes;

        $class_names = join(
            ' '
        ,   apply_filters(
                'nav_menu_css_class'
            ,   array_filter( $classes ), $item
            )
        );

        ! empty ( $class_names )
            and $class_names = ' class="'. esc_attr( $class_names ) . '"';



        $attributes  = '';

        ! empty( $item->attr_title )
            and $attributes .= ' title="'  . esc_attr( $item->attr_title ) .'"';
        ! empty( $item->target )
            and $attributes .= ' target="' . esc_attr( $item->target     ) .'"';
        ! empty( $item->xfn )
            and $attributes .= ' rel="'    . esc_attr( $item->xfn        ) .'"';
        ! empty( $item->url )
            and $attributes .= ' href="'   . esc_attr( $item->url        ) .'"';

        // insert description for top level elements only
        // you may change this
        $description = ( ! empty ( $item->description ) and 0 == $depth )
            ? '<small class="nav_desc">' . esc_attr( $item->description ) . '</small>' : '';

        $title = apply_filters( 'the_title', $item->title, $item->ID );

        $item_output = $args->before
            . "<a $attributes>"
            . $args->link_before
            . $title
            . '</a> '
            . $args->link_after
            . $description
            . $args->after;

        // Since $output is called by reference we don't need to return anything.
        $output .= apply_filters(
            'walker_nav_menu_start_el'
        ,   $item_output
        ,   $item
        ,   $depth
        ,   $args
        );
    }
}