In this paper, the model predictive current control (MPCC) is proposed to reduce the torque ripple of a switched reluctance motor by realizing precise current tracking. The Linear Quadratic Regulator (LQR) is employed to establish the cost functions of MPCC, which can select optimal control variables. Besides, the Kalman filter is employed to estimate the system state to reduce the influence of disturbance. In addition, the PI controller is replaced by automatic disturbance rejection control (ADRC) to further improve the robustness of the system. Finally, experimental results are shown to verify the effectiveness regarding distinguished tracking performance, dynamic response, and robustness of the proposed MPCC. It can be found that the improved MPCC proposed in this paper can achieve lower torque ripple, distinguished current tracking performance, and dynamic response performance.