Aiming at the problems of poor performance of finite-control-ser model predictive current control (MPCC) for permanent magnet synchronous motor (PMSM) caused by limited candidate voltage vectors and large calculation burden, a neural-network-based MPCC for PMSM was proposed. Based on the MPCC for PMSM with 7 basic voltage vectors and 121 extended candidate voltage vectors, the neural networks with 7 and 121 classification tasks were established. With the increase in candidate voltage vectors, the control performances of MPCC and the corresponding neural network were improved, but classification tasks were increased, too. For multi-step control, calculation burden will increase exponentially with the increase of steps, but output voltage vectors will not change. Therefore, a neural-network with 7 classification tasks was established based on two-step MPCC. Simulation results show all proposed neural networks operate well. And neural networks’ control performances are almost the same as the corresponding MPCC. Real-time experiments show that compared with one-step MPCC, the real-time performance of neural network is worse. But compared with two-step MPCC, the real-time performance of neural network is better and its calculation time is decreased by 29. 58% . Thus, neural network is more suitable for multi-step MPCC.