As for permanent magnet synchronous motor (PMSM) drive systems with dc-bus voltage sensor failure, a nonlinear function integral sliding mode (NFISM)-based finite-control-set model predictive current control (FCS MPCC) strategy with sensorless is put forward. In principle, measuring dc-bus voltage of voltage source inverter is vital for PMSM drives to perform FCS MPCC. Aiming at dc-bus voltage sensor unavailable, a new nonlinear extended state observer (ESO) is developed to estimate dc-bus voltage. In the light of load torque disturbance, a modified isokinetic reaching law is proposed and then outer loop NFISM speed regulator is brought forward to heighten the system robustness against load variation and attenuate the chattering level. What’s more, for the sake of decreasing the stator current ripple and improve dynamic response, an inner-loop FCS MPCC scheme is adopted. The proposed NFISM-based FCS MPCC with nonlinear ESO can make PMSM drives have satisfactory speed and torque performance. Compared with PI-based and ISM-based speed regulator, respectively, the proposed NFISM-based one enables FCS MPCC PMSM drive system to have stronger anti-load variation ability and weaker fluctuation. StarSim/Hardware experiments validate the feasibility and effectiveness of the proposed strategy.