The traditional finite control set-model predictive control (FCS-MPC) of multi-level inverters in grid-connected systems faces challenges in balancing multiple objectives and dealing with efficient modulation, which ultimately affects the system’s performance. To address this issue, a suspended capacitor voltage self-balancing five-level active neutral-point clamped (ANPC) inverter and an improved FCS-MPC control strategy were proposed. This strategy preprocesses all voltage vectors of the inverter through classification and screening, constructing a vector pool that meets various objectives and implements rolling optimization with fewer vectors within the control cycle. Without considering the weight coefficient allocation among the cost functions, the objective cost functions were normalized to allocate the action time of each optimization vector to form the vector sequence output, so as to meet the multiple performance requirements of the system at the same time. The proposed circuit topology of this inverter has a self-balancing operating mode of the suspended capacitor voltage, which can further simplify the FCS-MPC algorithm. The results of experimentation demonstrate that the improved FCS-MPC algorithm enables the novel five-level ANPC inverter to achieve grid-connected current tracking control, improve the balance of split DC bus midpoint and suspended capacitor voltage. The proposed method is feasible and effective, providing a new solution for model prediction in multilevel converters.