Abstract: In the process of high-speed machining of NC system, unnecessary inertial vibration is generateddue to the non-smooth speed or acceleration curve. A new kinematic smoothing algorithm is presented forhigh speed and high precision machining. The algorithm is based on the jounce limited acceleration profileand accurately calculates the optimal transition velocity and duration of the feed motion at the corner. Asmooth contour trajectory can precisely control through the contour error. The tool path can reach G3 continuous,and the acceleration curve can reach G1 continuous, achieving uninterrupted feed motion around thecorner, significantly reducing inertial vibration and feed impact. By comparing the Bézier curve interpolationalgorithm in X-Y experimental platform controlled by RTX8.0 in Windows 7 （2 GHz i5processor）, it isproved that the proposed algorithm is in the process of machining the tool path with 414.2 mm, the durationof the corner is reduced by 30%. The algorithm has significant potential in reducing machining time andimproving machining quality.