A ball joint structure is disclosed, which includes a socket with a containing opening, a ball disposed in the socket, a cover disposed at the containing opening, a protrusion disposed at an outer surface of the ball, a concavity disposed at an inner surface of the socket, and plural adjustable elastic screws screwed on the socket. The protrusion is moved in the concavity when the ball is rotated in the socket. The ball is gripped in the socket with a force provided by the adjustable elastic screws.