Can foreign nationals be members of the Board of Directors of a Non-profit organization basing in other country?

Yes, you may form a non-profit organization. Depending on your intended activities, you may qualify as tax exempt under Section 501(c) of the Internal Revenue Code. As a director, you'll have a fiduciary responsibility to the corporation to look out for its welfare. From a tax perspective, you must watch out for any instance in which you would gain personally from any transaction with the corporation. The tax terminology that can apply in such instances is known as "private enurement" or "private benefit". Significant tax penalties can apply if a prviate enurement has occurred. This is definitely an area where you want an experienced, competent tax lawyer or tax accountant working with you.