How can i listing current category and Featured Category post list?

I think you’re asking about your custom secondary loop affecting your main loop, correct?

query_posts() alters the main loop. A quick fix would be to call wp_reset_query() after your custom loop to reset the query data:

<?php wp_reset_query(); ?>

However, it’s more efficient and friendlier to use WP_Query() instead of query_posts() (especially if you’re making a secondary loop). This should be the equivalent of your provided code using WP_Query():

<?php
if ( is_category() ) {
    $current_cat = get_query_var('cat');
}

$args = array(
    'category__and' => array( 55, $current_cat )
);

$my_query = new WP_Query( $args );
?>

<?php while ( $my_query->have_posts() ) : $my_query->the_post(); ?>
    <li>
        <a href="https://wordpress.stackexchange.com/questions/83176/<?php the_permalink(); ?>"><?php the_title(); ?></a>  
    </li>
<?php endwhile; ?>

<?php wp_reset_postdata(); ?>

References:

http://codex.wordpress.org/Function_Reference/query_posts

http://codex.wordpress.org/Class_Reference/WP_Query

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