This paper presents a novel model predictive current control method for current source inverters (CSI) following the duality with voltage source inverters (VSI). The method is based on the discrete prediction model of the system, including the converter and output filter. The model is used to predict how the system variables will behave for each switching state of the converter. The predictions are evaluated using a cost function that weights the level of accomplishment of the control goals. The switching state with the best performance is then generated. The proposed algorithm predicts the output currents (including the output filter capacitors), ensuring sinusoidal current generation without the need for cascaded control loops, coordinate transformations, and modulation schemes found in traditional solutions. In addition, low switching frequency is imposed by including a new term in the cost function. Simulation results validate the proposed control scheme, with performance comparable to the traditional solutions, especially in terms of the current and voltage harmonic distortion.