In this paper multi-input Ćuk- derived buck-boost inverter is presented based on Model Predictive Control (MPC). The control technique is applied to multi- input Ćuk- derived buck-boost inverter because of the several features such as reduction of passive elements compared with two-stage topologies and the family of impedance inverters such as Z-source Inverter (ZSI), Quazi Source Inverter(QSI), T-Source Inverter (TSI), and Y-Source Inverter (YSI) .in addition , it is suitable for photovoltaic applications as it has the ability to boost the DC voltage from the PV cells and also invert it to AC voltage in the one stage. The model predictive control is applied in this paper to get a high response in the dynamic changes. In addition, more than one variable can be controlled in the same cost function, all the aforementioned features of the MPC can be achieved by using a technical called reducing horizon technique has been used. As the actual values are measured and compared with the reference for several solutions, the less accurate error will be given to use as action for the switched control. The power topology circuit and control algorithm have been validated by MATLAB/SIMULINK Software.