A socket structure includes a socket body, an O-ring, and a carbon-fiber tube. The socket body includes a driving section and an acting section coaxially connected to the driving section. The driving section has an outside diameter greater than an outside diameter of the acting section and a stepped portion is formed in outer circumference between the driving section and the acting section. The driving section and the acting section have end faces that are recessed inwardly to form a driving hole and an acting hole, respectively. The outer circumferential surface of the acting section is formed with a circumferential groove in which the O-ring is received. The carbon-fiber tube is fit over the outer circumferential surface of the acting section of the socket body and has an end in abutting engagement with the stepped portion and an internal circumferential surface in contact with the O-ring.