This paper introduces a modified Finite Control Set Model Predictive Control scheme (FCS-MPC) for a Permanent Magnet Synchronous Machine (PMSM). This paper is to investigate the idea of interpolation to obtain an extra six virtual switching vectors, in addition to the original 8 physical switching vectors existed for the controlling functions, and as a result, there are total twelve active vectors available for the evaluation of the cost function in the FCS-MPC. Simulation results and spectrum analysis of the proposed approach demonstrate the improvement over the conventional FCS-MPC.