In this paper, the speed tracking problem of the interior permanent magnet synchronous motor (IPMSM) of an electric vehicle is studied. A cascade speed control strategy based on active disturbance rejection control (ADRC) and a current control strategy based on improved duty cycle finite control set model predictive control (FCSMPC) are proposed, both of which can reduce torque ripple and current ripple as well as the computational burden. First of all, in the linearization process, some nonlinear terms are added into the control signal for voltage compensation, which can reduce the order of the prediction model. Then, the dq-axis currents are selected by maximum torque per ampere (MTPA). Six virtual vectors are employed to FCSMPC, and a novel way to calculate the duty cycle is adopted. Finally, the simulation results show the validity and superiority of the proposed method.