The performance of drive control technology for permanent magnet synchronous motor (PMSM) directly determined the performance of the whole motor drive system. Motor drive technology based on model predictive control (MPC) was gaining attention due to the fact that MPC technology could perform rolling optimization control for the multipleinput multipleoutput (MIMO) system and was easy to impose constraints. The researches done by domestic and foreign scholars on the current control of PMSM based on MPC in recent years were reviewed and summarized. Meanwhile, the current control technology based on single vector, double vectors and three vectors in the MPC was modeled and the current output waveform was analyzed. Finally, the advantages and disadvantages of current technologies was compared comprehensively, and some problems existing in the current technology and the main development direction in the future were discussed.