The unbalanced AC grid voltage can cause output current unbalance and output power fluctuation of nine-arm modular multilevel converter (9A-MMC). Besides, the distortion of arm current and the fluctuation of submodule capacitor voltage can be aggravated, which affects the safe operation of 9A-MMC. This paper firstly establishes the mathematical model of 9A-MMC under unbalanced AC gird voltage, simultaneously considering the unbalance degree of AC grid. Then, the influence of unbalance degree of AC grid on the arm current and submodule capacitor voltage in 9A-MMC is analyzed. Finally, the simulation results verify the accuracy of theoretical analysis. This paper can provide guidance on the design of circuit parameters and control schemes for the 9A-MMC under AC grid voltage unbalance.