Commercial photovoltaic microinverter topologies are normally composed of two stages: a step-up DC-DC stage and a step-down dc-ac stage. Nevertheless, to achieve high-ratio conversion, a high frequency transformer is used in the DC-DC stage, resulting in a bulky configuration with a high cost of implementation. To minimize these issues, a single stage boost inverter is proposed, composed by two bidirectional boost DC-DC converter. The control of this topology is complex due to its high non-linearity behaviour. Therefore, this paper presents a control methodology based on Finite Control Set Model Predictive Control (FCS-MP) algorithm with predictions of the system variables through the inverter model and an optimization process. Each boost DC-DC converter of the inverter is regulated to achieve an output signal composed of the sinusoidal wave with a dc bias. The main features of the boost inverter and predictive control are analysed. Simulations are shown in order to validate the proposed control and the converter for grid-connected PV applications.