The socket wrench for fast screw-up and screw-off of hex nut includes one hollow socket body. The hollow inner cylinder surface has one set of successively connected planes and curved curves to constitute the work contour of the socket, and the work contour is formed through eliminating partial inner cylinder surface material. The inwards raised cylinder surface contacts with the outer prismatic planes of the hex nut to apply force for screw-up or screw-off. The distance E between the rotating center of the work contour and any of the inward bosses is smaller than the hex nut size e, and there is some interval between the outwards cylinder surface of the work contour and the hex nut for the hex nut to rotate inside the socket within angle of 0-60 deg. The present invention is favorable to fast screw-up and screw-off of hex nut and has no sliding or clamping of the nut inside the socket.