Aimed at the problems that the output voltage overshot is high, the power factor is low, the convergence is difficult while the system parameters change, and interference with ac input current of Vienna rectifier by using traditional PI control is heavy, a global fast terminal sliding mode control strategy based on neural network is proposed. In view of the perturbation of the system parameters and the external disturbances in the actual environment, an uncertainty model of the system is reconstructed, the uncertainties are combined with the total disturbance, and the adaptive neural network is utilized for estimating it, and the Lyapunov theorem is used to prove that the nonlinear control system can achieve bounded stability under the perturbation of the system parameters and the external disturbances.The simulation results show that the proposed method can improve the power factor of Vienna rectifier, overcome the problem of output voltage overshot and effectively reduce the harmonic pollution of the system. Finally, a physical prototype is built, and the experimental results show that the above conclusions are correct.The method presented in this paper has no overshoot, and the steadystate response time, switching load voltage fluctuation, dynamic response time and harmonic content are reduced by 69%, 87%, 84% and 68% respectively.