Finite control set-model predictive control (FCS-MPC) is an interesting alternative for the control of drive systems. However, FCS-MPC requires a large amount of calculation, because it uses all feasible voltage vectors of a power converter for prediction and evaluation. This is an obstacle for its application when the number of voltage vectors of power converter is increased. The computational burden is more challenging when the control objectives are increased. At the same time, matrix converter is an attractive alternative to conventional back-to-back converters with dc link. However, implementation of FCS-MPC for a matrix converter is computationally expensive due to the 27 feasible voltage vectors of the matrix converter. In this paper, a Lookup table is used to reduce the candidate voltage vectors that make the FCS-MPC computationally efficient for matrix converter-fed permanent-magnet synchronous motors. This approach is implemented experimentally and is compared with the conventional approach to evaluate its performance.