Full-bridge modular multilevel converter (FBMMC) has strong ability to block DC fault current. It is more suitable for overhead lines and multi-terminal voltage source converter based HVDC system. This paper introduces the differences of startuping behaviors between FBMMC and HBMMC (half bridge modular multilevel converter). A sectionalized startup strategy is proposed and analyzed for FBMMC connected to active and passive system respectively. The startup strategy of passive network for black start is mainly studied. The proposed strategy is able to ensure a safe and reliable startup of the converter stations. In addition, the non-fault end of the system could work stablely. The validity of the proposed strategy is proved by PSCAD/EMTDC simulations.