The flexible HVDC transmission system based on a Modular Multilevel Converter (MMC) has attracted a lot of attention in recent years. The operation of an MMC under unbalanced grid voltage is studied, and an energy balance control strategy is proposed to improve the internal energy balance of the MMC under unbalanced grid conditions. By analyzing the coupling relationship between the bridge arm energy and electrical signals, a mathematical model of bridge arm energy is established in a coordinate system, and the anti-interference ability of the AC network under asymmetric faults and uneven burst voltage is improved by adding feed-forward compensation. The energy balance control of the bridge arm is carried out by optimizing the internal current component of the converter. This realizes coordinated control of AC side current and internal energy of the converter under an unbalanced network voltage. Finally, a two-terminal MMC simulation model is built on the platform of Matlab/Simulink. The simulation results verify the effectiveness of the proposed control strategy. This work is supported by National Natural Science Foundation of China (No. 51977014) and Science and Technology Project of Hunan Province (No. 2018KJ151).