Abstract: In order to reduce the effect of speed change on machining accuracy and efficiency, the numerical control system should have the function of speed control. In this paper, the cubic polynomial acceleration and deceleration control algorithm is adopted, and the interpolation principle of time division method is combined to give the detailed acceleration and deceleration control algorithm of straight line segment, circular arc segment and the transition track between them, and the acceleration and deceleration control strategy of micro line segment are provided. The algorithm mentioned in this paper is applied to the desktop open CNC lathe I participated in the research and development to ensure the flexible change of feed speed, thus verifying the feasibility of the algorithm.