This article proposes a fast-terminal cost index (FTCI) based continuous control set model-based predictive speed control (CCS-MPSC) to improve the tracking performance of CCS-MPSC. First, an extended surface-mounted permanent magnet synchronous motor model that incorporates parameter mismatches and external interference into a disturbance term is utilized to facilitate the determination of parameters and reduce computational complexity. Second, by introducing a differential feedforward term, an exponential convergence cost index (ECCI) based CCS-MPSC has a smaller lag error than conventional CCS-MPSC when tracking a given speed. Third, an FTCI, which simultaneously includes a terminal attractor, a differential feedforward term, and a lumped disturbance term, is developed to improve the tracking performance of ECCI further. Finally, a fast-terminal integral sliding-mode observer is designed to estimate the lumped disturbance and the differential feedforward term fast and accurately. Experiments of proportional-integral control, conventional CCS-MPSC, ECCI, and FTCI have been carried out on an FPGA-based hardware system, and the experimental results validate the excellent tracking performance of the FTCI strategy.