This report presents the proposal of finite control set model predictive control(FCS-MPC) for the control of the inverterswitching signals of a grid tied wind turbine back-to-back converter. Primary control objectives are tracking of DC-link voltage, and power references, in the contextof grid following. The controllers abilityto reduce inverter switching loses is alsoconsidered. Performance is compared toa PI controller representing the industrystandard. To facilitate predictive control,a model of the converter and filter dynamics is derived, and presented in state spaceform.Simulation of converter, filter and grid isperformed. Results does not shown meaningful performance advantages to suggestthe proposed method as a viable alternative to industry standard PI control. However, the prospect of further developmentand improvements discussed suggest itspotential.