Remove “Add New” link from custom post type

function.php

<?php 
function remove_submenus() {
    if(!current_user_can('activate_plugins')) {
    global $submenu;
    unset($submenu['edit.php?post_type=your_custom_post-type'][10]); // Removes 'Add New'.
    }
}
add_action('admin_menu', 'remove_submenus');

function hide_that_stuff() {
    if('your_custom_post-type' == get_post_type())
    echo '<style type="text/css">
    #favorite-actions {display:none;}
    .add-new-h2{display:none;}
    .tablenav{display:none;}
    </style>';
}
add_action('admin_head', 'hide_that_stuff');
?>