When MMC convertor operates in island model, if the power is supplied to the unbalanced load, especially single-phase load, negative sequence current will be generated. However, the existing island control strategy of MMC converter does not support the power supply demand of unbalanced load. To solve this problem, a novel island control strategy for MMC converter is proposed in this paper, which is suitable for the demand of unbalanced island load power supply. The control strategy includes two parts: positive sequence control and negative sequence control. The output of positive sequence control is the positive sequence component of modulation wave, which control the voltage amplitude of the PCC point. The output of negative sequence control is the negative sequence component of modulation wave, which balance the voltage drop on the impedance generated by negative sequence current, to make the negative sequence component of PCC point voltage zero. In this way, the PCC voltage will meet the requirements of national standard. Finally, a two-terminal MMC-HVDC system was set up in the platform of MATLAB/Simulink, and the effectiveness of the control strategy is verified.