This paper presents a finite control set model predictive current control strategy with a prediction horizon of one sampling time to control the single-phase matrix converter. The proposed current control strategy is based on a prediction calculation to select the switching states of the converter. By using a predictive cost function, the optimal switching state to be applied to the next sampling time is selected. This is done in order to obtain a good tracking of the load currents to their respective references. The feasibility of the proposed strategy is verified by simulation and experimental results, which show good dynamic and stationary performance.