On the invitation, let the people you invite know that it is to be a surprise. You could write "please keep this a secret" or something to that effect.
Write "TOP SECRET" at the top and then "You are invited to a surprise party to celebrate xxxxxx's birthday." Please keep it secret, he/she does not yet know!
Make sure you invite the guests far ahead of the guest of honor. Also make sure you write on it multiple times that it's a surprise, that guests need to be on time and not to tell!