Wind-farm-side modular multilevel converters (WFMMCs) used in modular multilevel converter based high-voltage direct current (MMC-HVDC) transmission systems must be able to control the AC grid voltage in offshore wind farms. Different AC voltage control strategies can significantly affect the dynamic characteristics of WFMMCs. However, existing studies have not provided a general methodology of controller parameter design, and few comparative studies have been conducted on control performance under varying operating conditions as well as the effects of different AC voltage control modes (AVCMs) on the stability of MMC-HVDCs with offshore wind farms. This paper provides a controller parameter design method for AVCMs, which is tested in various operating scenarios. Sequence impedance models of offshore wind farms and WFMMCs under different AVCMs are then developed. The effects of AVCMs on the small-signal stability of the interconnected system are then analyzed and compared using the impedance-based method. Finally, case studies are conducted on a practical MMC-HVDC system with offshore wind farms to verify the theoretical analysis.