wordpress custom post type remove duplicate menu item

Just added 'all_items' => __( '' ), in labels array.

Replace your code with below code

register_post_type('news', array(
    'labels' => array(
        'name' => __( 'News'),
        'singular_name' => __( 'News'),     
        'add_new' => _x( 'Add New News', 'News'),
        'add_new_item' => __( 'Add New News'),
        'edit_item' => __( 'Edit News'),
        'new_item' => __( 'New News'),
        'view_item' => __( 'View News Details'),
        'all_items'          => __( '' ),
        'search_items' => __('Search News')         
      ),
    'public' => true,
    'show_ui' => true,
    'menu_position' => 6,
    'has_archive' => false,
    'rewrite' => array('slug'=>'news'),
    'supports' => array('title', 'editor' ),
    'taxonomies' => array('category'),
    'menu_icon' => plugins_url('icons/news.png', __FILE__),
    )
);

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