A golf club grip is formed of a hollow, inner socket and an outer jacket produced from different charges of thermoplastic rubber. The socket and jacket differ in stiffness characteristics, colors, or both stiffness and color. The outer jacket is molded onto the socket and bonded thereto throughout the surfaces of contact therebetween. The torsional stress on the jacket is transmitted to and resisted by the inner socket through the bonding that occurs throughout the interface between the jacket and the socket. Preferably, the socket has an inner socket core portion with a plurality of radially projecting protrusions. The structure of the jacket laterally surrounds the protrusions so that the outermost surfaces of the protrusions are exposed. The golf club grip is produced from a pair of identical mounting cores which are rotated between a pair of molding dies. The sockets are first produced on one mounting core in a first die, and the first mounting core with the socket thereon is cyclically moved into the second die. While the jacket of the golf club grip of the invention is being molded onto the socket just produced in the first die, a new socket is concurrently produced on the second mounting core, which has been moved into the first die.