The invention relates to a method for reducing speed interpolation error and a hardware system, In order to meet the speed control requirement of the principle of machining high-order aspheric optical parts by a tangent method, the invention introduces a hidden Markov model (HMM) and provides a new speed foresight prediction compensation method. By the compensation method, the defects that acceleration and deceleration are frequent, and ripple traces are easy to leave on surfaces of aspheric workpieces in the conventional speed foresight compensation method are overcome, the continuous change of three-shaft speed is realized, speed error is reduced and positional precision is improved, so a continuous smooth curved surface without micro triple traces is acquired. The speed foresight compensation method also can be popularized and applied in other speed servo systems such as special equipment of artilleries, radar control, high-precision numerical control machines, robots, medical treatment equipment, semiconductor equipment and the like.