Unbalanced DC currents in parallel current source inverters cause unequal power division in the inverters, higher harmonic content at the AC load side and generally, system performance decline. In this paper, a novel Space Vector Modulation is introduced for a 5-level parallel current source inverter with DC current balance control. The method is working by synthesizing the rotating current reference vector in the inverter's space vector plane with three adjacent switching vectors. One Medium vector is employed as one of adjacent vectors to balance the input DC currents. The switching state for each switching vector is chosen to provide the balanced DC link currents. In addition, lower switching frequency is achievable due to switching design which minimizes the switching loss. Finally, effectiveness of the proposed method is verified by simulation.