Owing to its advantages such as high power density, low switch voltage stress and small grid current harmonic, the three-phase three-level Vienna rectifier has been widely applied to AC-DC hybrid power supplies including the data center DC power supply. However, the grid current performance of the three-phase Vienna rectifier strongly depends on the controller parameters, and unreasonable parameter values may often deteriorate the grid current, causing a worse anti-interference performance of the system. To effectively improve the static and dynamic performance of grid current, a novel kind of carrier-SVM control strategy based on the double closed-loop sliding mode variable structure is put forward. Furthermore, a modified exponential reaching law is adopted, and the neutral voltage DC fluctuation suppression strategy is given. To verify the correctness of the proposed sliding mode control (SMC) scheme, a complete simulation and experimental test model is established, and the detailed theoretical analysis and design scheme are given. Simulation and experimental results show that the proposed control strategy can effectively improve the dynamic and static performance of grid current while keeping the neutral voltage on DC side balanced.