To overcome the shortcomings of the conventional continuous control set model predictive current control (CCS-MPCC), such as large overshoot and poor robustness, an extended surface-mounted permanent magnet synchronous motor (SPMSM) model-based multistep error tracking CCS-MPCC (MSET-CCSMPCC) is proposed in this article. First, a traditional CCS-MPCC is derived based on the conventional SPMSM model and its robustness is analyzed by considering the parameter mismatches. Second, an extended SPMSM model is given by incorporating the lumped disturbances into one disturbance part. Third, a sliding mode differentiator improved fast terminal sliding mode disturbance observer is designed to track the disturbances. Fourth, by compensating the extended SPMSM model for the estimated d- and q-axes disturbances, an extended SPMSM model-based CCS-MPCC (EXM-CCSMPCC) is designed. However, the EXM-CCSMPCC has serious step response overshoot. Fifth, an extended SPMSM model-based single step error tracking CCS-MPCC is presented, whose dynamic response and steady-state performances deteriorate when the overshoot is reduced. Finally, an MSET-CCSMPCC is proposed to reduce the overshoot and improve the robustness while maintaining excellent dynamic and steady-state performances. Experiments are implemented on a field-programmable gate array based hardware system to verify the excellent performances of the proposed method.