Finite control set (FCS) model predictive torque control (MPTC) system of permanent magnet synchronous motor (PMSM) was built based on stator flux xycoordinates. Simulation results testified its effectiveness and feasibility. As stator flux and torque predictive models were complicated, simplified predictive models were given. Theoretical analysis, simulation and experiment results showed that FCSMPTC system using simplified models could achieve equivalent control performances as using conventional predictive models, but simplified model could decrease calculation burden and improve real time performance. A candidate voltage vectors set was proposed with variable amplitude and angle which were used as control variables in FCSMPTC. The proposed candidate voltage vectors set could suppress torque ripple at steady state, but its dynamic response was worse than that of conventional candidate voltage vectors set. Thus, an adaptive control strategy was proposed, which adaptively used different candidate voltage vectors sets at different states. Simulation results showed that the control strategy could achieve good control performance at both steady and dynamic states.