This research presents the development of a compact and cost-effective asymmetric multilevel inverter (MLI) that preserves the advantages of high-resolution multilevel systems while significantly reducing the component count. The proposed single-phase 31-level inverter configuration utilises only 2 isolated DC sources, 2 flying capacitors (FCs) and 10 MOSFET switches, achieving a notable reduction in both complexity and cost. A dedicated Finite Control Set-Model Predictive Control (FCS-MPC) strategy has been designed to regulate the FC voltages, ensure accurate reference current tracking and minimise switching losses. The weighting coefficients of the three components in the FCS-MPC cost function have been optimised to enhance the inverter’s overall performance. Using a one- step prediction horizon, simulation results demonstrate that the inverter achieves precise current tracking, with both RMS error and total harmonic distortion (THD) maintained <1%. The average switching frequency is approximately seven times the reference current frequency, indicating a considerable reduction in switching losses. The impact of extending the prediction horizon to two steps is also analysed with respect to switching losses and current tracking accuracy. Finally, a comparative evaluation with six recent high-resolution inverter designs confirms that the proposed system offers superior performance, achieving the lowest switch-to-level ratio, minimum total switch voltage ratings and capacitor voltage ratings, and the fewest series-connected switches per level in the current path.