Fault current limiting is a critical technology to ensure the safe operation of modular multilevel converter based multi-terminal direct current (MMC-MTDC) grids. This paper proposes a fault severity classification based coordination control strategy of fault current limiter (FCL) and MMC for adaptive fault current limiting. The proposed strategy reduces the investment in FCL, and keeps the bus voltages of non-faulty lines at reasonable values. Firstly, a rapid fault circuit parameter estimation (FCPE) method using initial fault current information is proposed. With this method, the fault distance and fault transition resistance can be quickly estimated, which are used for a quantitative indication of the fault severity. Subsequently, the coordination control strategy of FCL and MMC is proposed, in which the FCL action is prioritized, while the control of MMC is complementary for current limiting. Based on the proposed strategy, fault severity phase planes (FSPPs) are constructed to assess fault severity and calculate the activation time of FCL and voltage regulation factor of MMC. Therefore, the FCL activation and MMC control are matched to the fault severity. The effectiveness and advantages of the proposed strategy are validated by the simulations in PSCAD/EMTDC.