Private Server?

Is it Possible to make an Private Server of GTA Online?

Yes, Go onto story mode, next you will need to go to the start menu where you can then look upon the online settings where you would join an online match. Here you can find 2 options... Invite ONLY online and or solo online. Both describe them selves. enjoy.

PS - If your looking to do this for modding etc. You are still at HIGH risk of being banned.

Even in Private servers you will get banned. There is no difference between open and closed lobbies, you can cheat wherever you want.