A trampoline frame structure that comprises multiple transverse pipes, joint sleeve structures and leg arrangements is disclosed. The joint sleeve structures serve to connect transverse pipes to form a rim structure. Leg arrangements are connected to the joint sleeve structures. At the upper end of the joint sleeve structure is an elongated headpiece, and at both of the ends of the headpiece are sockets. The cross-section of the socket is polygonal. At the ends of the transverse pipes are conical connection extensions, and the cross-sections of the extensions correspond to the cross-sections of the sockets. The assembled rim structure comprises the transverse pipes with the headpieces between them.