A typical two-stage startup process of modular multilevel converter（MMC）is analyzed in detail，and the approximate calculation method of the limiting resistance is proposed.Detailed studies are given on the black-start scheme of the blackout terminal converter when MMC based high-voltage direct-current（HVDC）transmission system is used in grid black start.The corresponding start-up schemes for the two-terminal system and multi-terminal system are proposed.The proposed schemes can guarantee the secure and reliable realization of the converter black start without influencing the operation of other terminals.Finally，simulation models are established in PSCAD/EMTDC，the simulation results validate the efficiency of the proposed black start schemes for the converter of the blackout terminal.