This paper proposes a fault-tolerant operation scheme for modular multilevel converter (MMC) when a sub-module (SM) fault occurs. The MMC is featured with N-level corresponding to the number of SMs activated for an operation. The number of these SMs in the upper and lower arms should be the same, and the energy in each arm should be balanced during the normal operation state. The arm with faulty SMs however, results in the arm energy imbalance between upper and lower arms, and can cause an instability on voltage sourced-converter (VSC) control in the MMC by imbalancing the SM capacitor voltage, interrupting the power transfer. This paper thus first elaborates on the internal dynamics of MMC with faulty SMs analytically, and then develops a practical fault-tolerant operation scheme for non-interruptible power transfer. Rigorous simulation studies using PSCAD/EMTDC and PLECS demonstrate the validity and effectiveness of the proposed scheme. This research should help make the most of the topological redundancy in the MMC for the fail-safe power transfer.