Three-arc gear couplings are machine elements which can meet the requirements of high load-carrying capacity. Effectively enhancing the load-carrying capacity of gear couplings has been an important research objective. Three-arc tooth design solution is proposed that effectively improves tooth performance, an analytical model of the three-arc tooth geometry parameters is given, and a functional relationship between key design parameters and load-carrying capacity and wear performance is established in this paper. The radius of the displacement circle and the radians of the three arc segments are used to design the three-arc tooth, the working domain coefficient and the radians of large arc are constructed and used as core variables. Through the Hertz theory and numerical simulation model, the contact theory of the hub tooth surface with modified drum coefficient is proposed, and the clearance, equivalent stress and surface contact stress of the tooth under the action of misalignment angle are studied, and then the evaluation model of the load-carrying capacity and wear performance of the three-arc hub tooth is established. Compared with the single-arc tooth, the three-arc tooth can improve the load-carrying capacity under the premise of ensuring the strength, misalignment angle and size, and at the same time, the reasonable design of the three-arc tooth can improve the wear performance.