While the known modulation and control techniques for single-phase matrix converters are based on pulse width modulation or space vector modulation, this paper presents a finite control set model predictive control strategy with a prediction horizon of one sampling time to control the singlephase matrix converter. The presented converter is meant to be used in cascaded configurations for high power applications, as it has a three-phase input and a single-phase output. 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 results, which show good dynamic and stationary performance.