The paper proposes finite state model based current control of a three-level neutral point clamped (NPC) five-phase voltage source inverter. The space vector model of a five-phase voltage source inverter (VSI) yield 243 space vectors, with 240 active and three zero vectors. The presented technique utilizes only 21 space vectors for the current control and hence the name finite state is given. Search is made by the algorithm to find the vector which minimizes the chosen cost function. The performance of the current control heavily depends upon the choice of the cost function, the number of vectors used and the sampling time. The developed technique is tested for RLE load using simulation approach. The proposed technique offers very good capacitor voltage balancing and offers high performance results in terms of current distortion. The technique is very useful for real time implementation due to a small number of vectors being used in contrary to space vector PWM where at least 43 vectors are required to obtain similar results. Simulation results are given in the this submission, while the experimental validation of the concept will be provided in the final paper.