Model predictive control (MPC) is a well-known control methodology in power electronics systems, due to its ability to deal with the system's nonlinearities and superior dynamic response. MPC is able to handle multiple variables by adjusting the cost function, but this leads to high computational costs, especially for systems having a big number of switches. This problem increases when not only performance efficiency is required but also minimizing the power losses of these systems. In this paper, a modified MPC algorithm is presented for controlling a three-phase quasi Z-source inverter (qZSI), i.e., providing switching states to be applied for qZSI control, so that, within less computation time, total harmonic distortion (THD) of the output currents is maintained at the minimum level with concurrent minimization of inverter switch power losses. The computational burden is reduced by using calculation loop optimization, reducing the number of switching states in the loop and unrolling the calculation loop. To highlight the effectiveness of the proposed control methodology, a numerical simulation was carried out using MATLAB software. The obtained results have been discussed and compared with those of a recent previous study.INDEX TERMS Model predictive control (MPC), quasi Z-source inverter (qZSI), switching losses, conduction losses, total harmonic distortion (THD).