DC fault protection is the bottleneck that restricts the development of modular multilevel converter based high voltage direct current (MMC-HVDC) system. Superconducting fault current limiters (SFCL) is an ideal protection device that can significantly limit short circuit current and enhance the fault tolerance ability of MMC-HVDC system. At present, several topologies of SFCLs have been proposed, but there is no systematical study of their current-limiting characteristics in MMC-HVDC. This paper studies the development process of DC short-circuit faults in MMC-HVDC system, and analyzes its demand for fault current limiting. Then, resistive type, saturated iron core type and hybrid type SFCL are modeled and their limiting effect of critical fault current under DC pole-to-pole fault is tested. By comparison, the current-limiting characteristics of three types of SFCL are concluded. Results show that resistive SFCL has best performance in steady state, while saturated iron core SFCL has best performance in transient state. The current-limiting characteristic of hybrid type SFCL is between the other two types.