disable_addNew_custom_post_type.php

function disable_new_posts() {
// Hide sidebar link
  global $submenu;
  unset($submenu['edit.php?post_type=CUSTOM_POST_TYPE'][10]);

// Hide link on listing page
  if (isset($_GET['post_type']) && $_GET['post_type'] == 'CUSTOM_POST_TYPE') {
    echo '<style type="text/css">
    .page-title-action { display:none; }
    </style>';
  }
}
add_action('admin_menu', 'disable_new_posts');