This paper presents a novel model predictive control method for current source converters (esC) following the duality with voltage source converters (VSC). In vse the predictive control is applied to the output current, while in this work the esc is controlled through the output voltage. The method is based on the discrete prediction model of the system, including the converter and output filter. The model is used to predict future behavior of the system variables for each switching state of the converter. The predictions are evaluated in a cost function that weights the level of accomplishment of the control goals. The switching state with best performance is then generated. The proposed algorithm predicts the output terminal voltages (includes the output filter capacitors), ensuring sinusoidal voltage generation without the need of cascaded control loops, coordinate transformations and modulation schemes found in classic solutions. In addition, low switching frequency is imposed by including the switching frequency in the cost function. Simulation results show a preliminary validation of the proposed control scheme, with comparable performance to the classical solutions,