Hi Juraj,
Thanks for your attention on this issue.
I removed the permission for Media Library Module. However, if i un-check the "Can manage the group" for the role or user, They couldn't see any media libraries in this group no matter whether this role/user has the full permission (security tab when edit media library) or not.
By the way, can I add site related media library instead of group media library on live site?
Thanks