With high penetration of power inverters in microgrids, the Fault Ride-Through (FRT) strategy is of great importance for the inverter operation. However, the Finite Control Set Model Predictive Control is considered as a powerful control for power electronic devices and inverters. This control technique has not been applied for handling the FRT of stand-alone inverters. Therefore, this paper proposes a new control algorithm based on Finite Control Set Model Predictive Control to control the stand-alone inverter in normal modes and to ride-through the fault without any deterioration. The proposed algorithm considers the following aspects: high-speed fault detection, limiting fault current, power quality during the fault, and soft recovery to normal mode at the fault clearance. These aspects require additional calculations in the control algorithm, resulting in higher computation time and delay. In this paper, the delay is compensated using the two-step prediction horizon principle. Moreover, the algorithm is optimized by removing repeated computations and by separating the fault mode algorithm from the basic algorithm. Simulation and experimental studies are carried out to validate the performance of the proposed FCS-MPC algorithm under symmetrical and asymmetrical faults. The results reveal the high effectiveness of the proposed algorithm to improve the FRT capability of the inverter.