In order to remove flaws from the edge of mobile phone cover glass for improving its impact resistance, a CNC edge grinding machine was designed. The Linear interpolation algorithm and the circular arc interpolation algorithm, based on the polar coordinates system, were proposed, in which the geometrical analysis method was used, by aiming at the outline of the mobile phone cover glass. Some key factors which had an important effect on the processing accuracy were discussed. The formula of tracking error for discrete time system and comprehensive contour error were deduced. The cubic spline interpolation method was carried out to perform dynamic simulation of constant angular velocity grinding based on the platform of MATLAB software. Furthermore, the improved strategy was put forward about constant angular velocity grinding. The practice has proven that it can effectively improve the edge grinding accuracy and meet the requirement of the grinding technique by using above control algorithm. 