This paper proposes a model predictive control method based on Kalman filter (MPC-KF) for solving the challenges in simultaneous control of output current tracking, capacitor voltages balance, and harmonic circulating currents suppression, and the operation reliability affected by the damaged sensors regulated modular multilevel converter (MMC), which aims to realize the multi-objective control, enhancing the operation reliability of MMC system. Firstly, the MPC principle of MMC is described. Then, the capacitor voltage prediction-correction strategy based on Kalman filter with only arm current sensor is proposed to obtain the capacitor voltage correction value, instead of using lots of submodule (SM) voltage sensors. In this sense, the reliability under sensor failures of system can be improved. Finally, compared with the SM voltage estimation strategy with single voltage sensor and the conventional SM capacitor voltage measurement strategy, simulation studies are illustrated to demonstrate the feasibility and effectiveness of the proposed MPC-KF method for MMC.