When the voltage of the grid is unbalanced, it is difficult to use traditional control methods for the unified power quality conditioner(UPQC) of a modular multilevel converter(MMC) to comprehensively control the power quality, and the compensation efficiency and accuracy are low. To solve these problems, a passive super-twisting second-order sliding mode control strategy is proposed. Firstly, based on the mathematical model of the MMC-UPQC and passive control theory, a positive and negative sequence passive controller based on the Euler-Lagrange model under unbalanced power grid voltage is designed. Then, super-twisting second-order sliding mode control is added to improve the passive controller, which suppresses chattering of the conventional sliding mode, and solves the problem that passive control requires high precision of the system. It improves the response speed, compensation accuracy and anti-interference ability of the system, and improves the overall performance of the system. Finally, the simulation is carried out on the Matlab/Simulink platform and compared with PI control and independent passive control. Simulation results verify the effectiveness and superiority of the proposed passive super-twisting second-order sliding mode control strategy.