For modular multilevel converter (MMC) based high-voltage direct-current (HVDC) system, its dynamic simulation faces the problems of cumbersome construction, small simulation step and extremely time-consuming. Based on the review of the results of existing research, four equivalent models are proposed for accurate and accelerated simulation. The four types of equivalent models are investigated by comparative study. All equivalent models are compared with the original detailed MMC’s circuit model. Their key characteristics in simulation are examined. The key characteristics include the simulation speed, the required minimum simulation step and the accuracy for different stability studies (for instance, low-frequency oscillation, short-circuit fault and sub synchronous oscillation). The comparative study of different models provides a reference for selecting a reasonable equivalent model for different targets and requirements. And the results of this work lay a foundation for further improvement on equivalent models of MMC-based VSC-HVDC systems.