In response to the issues of slow response speed and poor anti-disturbance performance of traditional control methods for three-phase Vienna rectifiers under system load variations and grid-side voltage fluctuations, as well as the problems of chattering and steady-state errors associated with commonly used sliding mode control, a control strategy based on second-order nonsingular terminal sliding mode and model predictive control is proposed. The second-order nonsingular terminal sliding mode control is introduced into the voltage outer loop to achieve rapid recovery and stable output of the DC-side voltage under load disturbances and grid voltage fluctuations. The model predictive current control is adopted in the inner loop to enable the input current to have fast tracking speed while maintaining low harmonic distortion. Simulation and experimental results verify the feasibility and effectiveness of the proposed control strategy.