To solve the ring-shaped corrugation error problem existing in the machining of aspherical optical components,the basic principle of CNC tangential rotary forming aspherical machining was explained,the mathematical modeling process of the application of the velocity interpolation principle was analyzed.Due to the time-based nature of the feed,a scheme of constructing a for ward-looking prediction model for speed was proposed combining the hidden Markov model,and a hidden Markov compensation model was constructed based on the actual aspherical processing samples.The experimental results show that the speed forward-looking compensation technique based on hidden Markov model can effectively realize the speed compensation in the speed interpolation,the speed error residual can be reduced to 0.949 8 after compensation,which meets the machining accuracy requirements of the aspheric CNC grinding machine.