There exists large zero sequence current flowing through interconnected AC grids by the path of transformerless MMC-HVDC system under AC grid unbalanced fault conditions, which has unfavorable influence in both the MMC-HVDC system and AC grids. Based on the MMC average model, the simplified zero sequence equivalent network of MMC-HVDC is derived in this paper, and the relation between the zero sequence voltage and current is deduced. The zero sequence current effect mechanism is consequently explained. An additional zero sequence current controller (ZSCC) based on the proportional-resonant module is adopted, which can effectively suppress zero sequence current and enhance the fault ride-through capability of the transformerless MMC-HVDC system. The accuracy of the above theoretical analysis and the effectiveness of ZSCC are validated by PSCAD/EMTDC simulation results. This work is supported by Science and Technology Project of State Grid Corporation of China "Key Techniques Research and Demonstration Application of Flexible Loop-network Controller"(No. 2014GW-05).