Three-phase, three-level Vienna rectifiers are widely used in power supplies for the advantages of high power density, low switching voltage stress and low grid side current harmonics. However, due to the presence of positive and negative sequence components under the unbalanced weak power grid, the control structure using the traditional proportional integral (PI) control is complicated and requires decoupling and multiple coordinate transformations, and it has longer dynamic response time. This paper presents an unbalanced current control strategy that combines improved sliding mode control (SMC) with new reaching law and multi proportional resonance (MPR) control of Vienna rectifier under unbalanced weak power grid. This paper establishes the mathematical model of Vienna rectifier under unbalanced weak current network. In the αβ coordinate system, dual second-order generalized integrator (DSOGI) is used to separate the positive and negative sequence components of the voltage. Suitable sliding mode surfaces and sliding mode convergence laws were designed. Finally, the results of simulations and experiments were used to verify the effectiveness of the proposed method.INDEX TERMS multiple proportional resonant (MPR) control, positive and negative sequence separation, second harmonic components, sliding mode control (SMC), unbalanced weak power grid