As to the low dynamic response of tangential follow system, especially the poor dynamic follow ability when executing small arc rapid interpolation. Based on the principle of mechanical dynamics, the mathematical model of leather cutting machine tangential follow mechanical transmission system is built, considering a type of high-speed numerical control leather cutting machine as the research object. Joined mechanical model and servo motor model together, its electromechanical combined system diagram is created by Simulink. On the basis of this diagram, the dynamic characteristic is analyzed. The composite evaluation standard including multiple performance indexes is used for the fitness function, the three-ring PID control parameters of tangential follow system is optimized with genetic algorithm (GA). The results show that GA optimization is more superior and efficient, comparing with traditional PID setting method.