The short-circuit fault of MMC-MTDC has great influence on the safe and stable operation of the MMC-HVDC transmission system. To analyze the changing trend of short-circuit current after fault, this paper studies the short-circuit fault mechanism based on the analytical formula of MMC short-circuit current, and analyzes the influence of capacitance, inductance and resistance on short-circuit current. Subsequently, the discharge characteristics of each converter station in multi-terminal complex power grid under different fault conditions are investigated. Based on the above research, a general calculation method for short-circuit current of multiterminal complex direct power grid is proposed. Then, a four-terminal power grid and a six-terminal power grid are built based on the PSCAD/ EMTDC electromagnetic transient simulation platform to verify the fault characteristics of MMC and discharge characteristics of multi-terminal network converter stations respectively. Finally, a digital-physical hybrid simulation experiment platform is erected to verify the effectiveness of the analytical calculation method for short-circuit current. The results demonstrate that the theoretical solution method can accurately characterize the fault current variation trend, which has an extremely important guiding significance for the engineering design and control protection of MMC-HVDC transmission network.