In order to improve the wide-range speed regulation accuracy and dynamic response performance of the permanent magnet synchronous motor system, and solve the problems that it is difficult to adjust the weight coefficient of traditional cost function in predictive speed control, this paper proposes a fast predictive speed control strategy for PMSM system without weight coefficient, and proposes a new regulation range widen method combined with voltage vector optimization. Firstly, the discrete model of PMSM is established, and then the reference voltage vector is predicted. Then, the cost function is improved to the voltage dimension to eliminate the weight coefficient, and the alternative vectors are selected according to the sector position of the reference voltage vector, so as to shorten the calculation times. At the same time, to widen the speed regulation range, the current limit and voltage limit are analyzed from the perspective of α-β coordinate combined with voltage comparison method, and the current and voltage limit are realized supplemented by the correction of the voltage vector adjustment time. Finally, the experimental study proves that the proposed control strategy can meet the dynamic and steady-state requirements of wide-range speed regulation without the weight coefficient.