Asymmetrical hybrid cascaded (AHC) multilevel inverters (MLIs) adapt in medium- and high-power applications due to their good output voltage performance and numerous voltage levels. Research on reliable control schemes for AHC MLIs is necessary due to complicated practical conditions. This study presents a finite control set–model predictive control (FCSMPC) algorithm for a three-phase AHC MLI. The topology has few switching component requirements and generates many voltage levels through changes in the DC power supply ratio. FCS-MPC is designed for AHC MLIs to achieve stable and reliable control. Delay compensation and computational burden relief are also realized. Simulation and experiment results confirm the good performance of the proposed algorithm for AHC MLIs under steady-state and dynamic processes.