This article proposes a novel integral sliding mode (ISM)-based model predictive current control (MPCC) strategy with low computational amount for three-level neutral-point-clamped (3L-NPC) inverter-fed PMSM drives. For conventional MPCC for 3L-NPC inverter, 27 voltage vectors are evaluated for prediction and calculation in each control cycle, therefore computational burden is a major hurdle for practical implementation of MPCC. With only calculation of reference voltage and determination of its sector position, a revised MPCC strategy with neutral point potential (NPP) balancing is proposed, which not only dramatically reduces the number of candidate voltage vectors involved in cost function calculation but also effectively suppresses NPP fluctuation of 3L-NPC inverter. To enhance MPCC robustness against motor parameter variations, the integral sliding mode (ISM) is embedded into MPCC for PMSM drives by enforcing sliding mode throughout the entire system response, and thus a novel ISM-based MPCC strategy is put forward. Furthermore, its robust stability is analyzed. The results of simulation experiments confirm that the proposed ISM-based MPCC strategy with NPP balancing for 3L-NPC inverter can enable PMSM drive system to have satisfactory control performance and strong robustness against motor parameter variations.