The multilevel converter has many advantages, and for that reason, they are widely used in medium and high power applications. On the other hand, finite set model predictive control (FS-MPC) is presented as a suitable control strategy for multilevel converters because it can manage many control goals with a simple cost function. However, FS-MPC needs to evaluate all of the voltage vector's actuation in the power converter, and in multilevel topologies this can result in a high computational effort. This paper proposes a geometrical method based on the predictive model to reduce the number of vectors that must be evaluated when using the FS-MPC strategy. The method is validated using a four-level three-cells flying capacitor converter, that has 512 voltage vectors. In its poorest performance, the proposed method reduces the computational effort to 35% of that used to evaluate the complete case (512 voltage vectors). Simulation results are presented to validate the proposed control strategy.