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This paper presents a model predictive current control algorithm that is suitable for multilevel converters and its application to a three-phase cascaded H-bridge inverter. This control method uses a discrete-time model of the system to predict the future value of the current for all voltage vectors, and selects the vector which minimizes a cost function. Due to the large number of voltage vectors available in a multilevel inverter, a large number of calculations are needed, making difficult the implementation of this control in a standard control platform. A modified control strategy that considerably reduces the amount of calculations without affecting the system's performance is proposed. Experimental results for five- and nine-level inverters validate the proposed control algorithm.