The modular multilevel converter (MMC) holds promise as a power supply solution for AC-AC conversion in railway traction systems. This paper introduces a indirect finite control set model predictive control (FCS-MPC) approach aimed at enhancing the dynamic performance of the converter. A discrete-time domain state space model is developed to forecast the behavior of both the three-phase side currents and circu-lating currents one step ahead. A cost function is defined to determine optimal insertion indices in each phase, facilitating rapid current tracking. Additionally, controls for phase and arm module capacitor voltages are implemented to further improve performance. Simulation results validate the effectiveness of the proposed strategy, highlighting its superior performance compared to traditional control methods.