This paper presents a medium-voltage drive based on an open-end winding induction machine supplied by a multilevel power converter topology. The power converter consists of cascaded two-level three-phase voltage source inverters (VSI) connected to each side of the machine windings and each VSI is fed by an isolated DC supply. The topology has been previously reported in the literature as a sinusoidal pulse-width modulation operating in an open loop. In this work, a closed-loop model predictive control (MPC) strategy is proposed. MPC offers a much simpler method to control the power switches of the inverter compared to complex modulation strategies that are typically used in multilevel converters. Moreover, the advantage of reducing the common-mode voltage offered by the open-end winding configuration is fully exploited in this work. Simulation results are presented to validate the performance of the proposed topology and control method.