The model predictive control (MPC) of voltage source pulse width modulation (PWM) rectififier is extremely dependent on system model in control process. System model mismatch will make the prediction results deviate from the actual value, seriously affect the system control results, even caused the system to be unstable. In addition, MPC is a control method based on state space model and predictive state of controlled system. In each control cycle, it performs an ergodic optimization to solve the online optimization, and thus determines optimal driving signal of the switching device. However, to obtain the optimal control variables online usually leads to a high amount of computation, which is one of the difficulties in the implementation of MPC on PWM rectifier. To solve these problems, neural network is used to approximate the unknown functions in system model. A finite set model predictive path integral control (FCS-MPPIC) based on neural network is proposed to effectively decrease computational complexity of control algorithm under premise of ensuring the distortion rate of the grid side current. At the same time, dynamic response speed of the system is improved. Finally, the availability of this method is verified through the simulation results.