To address the issues of slow dynamic response and large current ripple in traditional control of permanent magnet synchronous motors, an improved model predictive control algorithm is proposed based on a novel dual-power sliding mode integral speed controller optimized by the slime mold algorithm. First, the velocity loop adopts a new double power convergence law sliding mode velocity controller to control the motor more accurately. The stability of this method is validated using the Lyapunov function. Second, the slime mold optimization algorithm is applied to optimize the parameters of the dq-axis PI controller, enabling rapid determination of the optimal PI parameters. At the same time, current model predictive control is employed to reduce current ripple. Finally, from a microscopic perspective, a 3D phase diagram of dq-axis current and motor speed (n) is drawn to further verify the effectiveness of the controller. Simulation results show that compared with the traditional PI-MPC, SMC-MPC and NSMC methods, the proposed method NSMC-MPC has significant advantages in dynamic response speed, speed stability and anti-interference ability, which can significantly reduce the overshooting and current pulsation, and improve the dynamic performance and load adaptability.