This paper presents a multi-objective Model Predictive Control (MPC) for a grid connected 2-cell 5-level quasi Z-Source (qZS) Cascaded H-Bridge (CHB) inverter. The main contribution of the proposed control approach is the design of a multi-constraint cost function to achieve multi-objective MPC strategy dealing with the complex nature of the presented qZS-CHB topology. The designed cost function takes into account three control objectives, which are the minimization of the grid current, input current, and capacitors' voltages tracking errors. The best performance scenario is realized through the fine tuning of the constraints' weighting factors based on the grid current's error minimization and the reduction of the double-line frequency ripples on the input current. As a result, the proposed scheme achieves high-quality tracking of the encompassed state variables with the elimination of the double-line frequency power flow through the qZS inductors leading to the reduction of the hysteresis losses and the increase of the overall system efficiency. The performance of the proposed MPC strategy has been investigated and compared to the state of art PI controller. Theoretical analysis and implementation results are given to show that the proposed scheme is suitable for all system configurations and has good performances even during disturbances. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.