This paper presents a new control strategy for a four-leg indirect matrix converter that effectively mitigates common-mode voltages and gives optimal control of source and load currents. This method uses the commutation state of the converter in the subsequent sampling time according to an optimization algorithm given by a simple cost function and a discrete system model. The control goals are the regulation of the output current according to an arbitrary reference and tracking of the source current reference, which is imposed in order to obtain sinusoidal waveforms with low distortion. The technique is enhanced by a reduction of the common-mode voltage using an extra term in the cost function to reduce early motor winding failure and bearing deterioration. Simulation results are presented to support the theoretical development.