Abstract: In order to improve the anti-interference ability for the rectifier and reduce the adverse effect on the power grid, T-typed Vienna rectifier is adopted to implement the comprehensive control of the DC voltage output and the AC current inputs. Based on the mathematical model of the three-phase T-typed Vienna rectifier, a passivity-based controller for the current tracking algorithm with nonlinear virtual damping injection is proposed to realize the tracking of the command current at a high speed, and with high accuracy and low harmonic distortion; The active disturbance rejection control(ADRC) algorithm with nonlinear control on the DC side voltage error is adopted to improve the ability of the rectifier output voltage to resist load disturbance and grid voltage fluctuation, and realize the output voltage stability and fast recovery. Compared with the typical voltage PI + current PI or the traditional passivity-based current control strategy, the proposed algorithm makes the Vienna rectifier operate with high power factor, with low harmonic distortion, stable DC output voltage, and strong resistance to the load and grid voltage disturbance. The simulation and experimental results verify the feasibility and effectiveness of the passivity-based control with nonlinear virtual damping and the active disturbance rejection control strategy for the T-typed Vienna rectifiers.