The double-star converter (DSC) is a recently introduced medium-voltage 4-level multilevel inverter topology, with a reduced number of active switches. This topology has several advantages over existing commercial topologies (single dc-source, no clamping elements, no bidirectional switches or flying capacitors), which can satisfy the needs of several medium voltage applictions such as pumps, fans and compressors. The main challenge with this topology is the voltage balance of the three dc-link capacitors across the modulation index range. Classic controllers require sophisticated PWM techniques with closed loop compensation to maintain the capacitor voltages balanced. In this paper, a control algorithm based on model predictive control (MPC) is applied to the DSC, allowing a direct regulation of the converter output currents while simultaneously ensuring the dc-link capacitors voltage balance. Simulation results show the effectiveness of MPC when applied to this converter.