A Matlab/Simulink model for the Finite Control Set Model Predictive current Control FCS-MPC based on cost function optimization, with current limit constraints for four-leg VSI is presented in this paper, as a new control algorithm. The algorithm selects the switching states that produce minimum error between the reference currents and the predicted currents via optimization process, and apply the corresponding switching control signals to the inverter switches. The new algorithm also implements current constraints which excludes any switching state that produces currents above the desired references. Therefore, the system response is enhanced since there is no overshoots or deviations from references. Comparison is made between the Space Vector Pulse Width Modulation SVPWM and the FCS-MPC control strategies for the same load conditions. The results show the superiority of the new control strategy with observed reduction in inverter output voltage THD by 10% which makes the FCS-MPC strategy more preferable for loads that requires less harmonics distortion.