Abstract: The MMC-UPQC system formed by unified power quality controller (UPQC) and modular multi-level converter (MMC) can be used for the compensation control of current and voltage at medium and high voltage and high power. However, at present, the MMC-UPQC generally adopts PID linear control methods to carry out the compensation control of current and voltage. The MMC-UPQC is a nonlinear and multivariable object, thus linear control methods such as PID are difficult to obtain satisfactory compensation quality. Therefore, this paper proposes a nonlinear Lyapunov function control method for compensation control of MMC-UPQC current and voltage under unbalanced grid voltages. First, mathematically model for MMC-UPQC under unbalanced power grid is established; next, the positive and negative sequences of electrical quantities on series and parallel sides of MMC-UPQC under unbalanced grid are separated; the Lyapunov function control method is used for power quality compensation of MMC-UPQC under unbalanced grid voltage, the stability of Lyapunov function control system is proved, and the stable range of Lyapunov function control gain is introduced. Finally, the two methods of Lyapunov function control and traditional PID control are compared on the simulation system platform. The simulation results verify that the Lyapunov function control method can be adopted to better compensate the power quality of MMC-UPQC current and voltage.