Aiming at the problem of large commutation torque ripple of brushless direct current motor (BLDCM) under six-pulse drive mode, a torque ripple suppression algorithm based on finite set model predictive control (FCS-MPC) is designed. Firstly, the characteristics of non-commutation current are predicted. Then, the value function is used to select the best switch state of driving circuit to suppress the ripple of the non-commutation current. The experimental results show that, when using the torque ripple suppression algorithm designed in this paper, the torque ripple deviation ratio of BLDCM is 4.04% at high speed and 0.88% at low speed, which means that the algorithm designed in this paper has good commutation torque ripple suppression effect whether the motor is running at high speed or low speed.