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A global fast terminal sliding mode(GFTSM)-based model predictive torque control(MPTC) strategy is developed for permanent magnet synchronous motor(PMSM) drive system with only one phase current sensor. Generally two phase-current sensors are indispensable for MPTC. In response to only one phase current sensor available and the change of stator resistance, a novel adaptive observer for estimating the remaining two phase currents and time-varying stator resistance is proposed to perform MPTC. Moreover, in view of the variation of system parameters and external disturbance, a new GFTSM-based speed regulator is synthesized to enhance the drive system robustness. In this paper, the GFTSM, based on sliding mode theory, employs the fast terminal sliding mode in both the reaching stage and the sliding stage. The resultant GFTSM-based MPTC PMSM drive system with single phase current sensor has excellent dynamical performance which is very close to the GFTSM-based MPTC PMSM drive system with two-phase current sensors. On the other hand, compared with proportional-integral(PI)-based and sliding mode(SM)-based MPTC PMSM drive systems, it possesses better dynamical response and stronger robustness as well as smaller total harmonic distortion(THD) index of three-phase stator currents in the presence of variation of load torque. The simulation results validate the feasibility and effectiveness of the proposed scheme.