Aiming at the corner connection speed of continuous small blocks caused by their angle influences, the speed of transition is low and easy to cause vibration of machine tool. Research on the mathematical model of constant-speed linking of multiple periods is established by using the arc to smooth continuous small blocks, combined with the transition’s geometrical constraint, motion constraint, parameter calculation, the theory is to realize the method of high-speed interpolation of constant-speed linking of multiple periods. The result reveals that the effectiveness and practicability of the proposed method.