This research presents the development of a compact, cost-effective multilevel inverter that preserves the advantages of high-resolution multilevel systems while reducing the component count. The proposed single-phase 31-level inverter configuration utilizes two isolated DC sources, two capacitors, and ten 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 flying capacitor voltages, ensure accurate reference current tracking, and minimize switching losses. The weighting coefficients of the three components in the cost function have been optimized 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 maintained below 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 analyzed with respect to switching losses and current tracking accuracy. A comparative evaluation with six recent high-resolution inverter designs confirms that the proposed system offers superior performance, achieving low switch-to-level ratio, minimum switch and capacitor voltage ratings, and the fewest series-connected switches in the current path.