Model predictive current control (MPCC) suffers from high computational effort, and control performance is affected by parameter mismatch. In this paper, a robust MPCC strategy with low complexity for permanent magnet synchronous motor (PMSM) is proposed, which reduces the computational complexity and improves robustness. First, a low-pass filter is used to obtain the current actual voltage, and the next-cycle voltage vector is obtained by angle compensation. Alternative voltage vectors (AVVs) are selected according to the location of the next-cycle voltage vector to reduce the control system computation. This part does not use motor parameters to avoid the influence of parameter changes. Then, the relationship between the current error and the input voltage and current sampling value is analysed. A low-complexity current prediction error compensation algorithm is designed to compensate the error caused by the mismatch of motor inductance and flux linkage, which enhances the robustness of the system. Finally, the experimental results demonstrate the correctness and effectiveness of the proposed strategy.