Predictive torque control (PTC) is one of the most widely discussed strategies for high performance permanent magnet synchronous motor (PMSM) drive system because of its fast dynamic response and good stability. However, the complex prediction and optimization process requires a large amount of computation. Until now, few studies have carried out any systematic research on the simplification of the PTC. In this paper, a stepwise simplification method for the PTC strategy is proposed. Firstly, by using the equivalent transformation, the prediction process is simplified without affecting the control performance of the PTC. On this basis, the cost function is further simplified with additional presuppositions, and the optimization process is replaced by honeycomb-structured space partitioning for optimal voltage vector searching. Therefore, the computation burden caused by the multiple calculations in traditional PTC is greatly reduced. In addition, this paper provides the implementation details of the proposed control strategy. Moreover, the comparison between the traditional PTC and two simplified PTC is carried out in the evaluation of the transient performance, steady-state errors, control characteristics, computation burden, and compatibility with additional constraints. The experimental results prove the feasibility and effectiveness of the simplified algorithms, and this is beneficial to the future application of PTC strategy in the low-cost motor drive system. Moreover, the simplified PTC algorithm can achieve higher switching frequency, thereby improving the performance of torque and stator flux in the motor drive system with the application of new generation SiC power device. INDEX TERMS PMSM, predictive torque control, computation burden, cost function.