Finite states model predictive control (FS-MPC) appears as a promising control technique to be applied to power converters in the industry. However, the FS-MPC presents some drawbacks as non constant switching frequency and high sampling frequency. This work proposes a FS-MPC with constant switching frequency and low sampling frequency applying a discrete space vector modulation (DSVM) technique. The real state vectors of the converter are used together with new virtual state vectors forming switching sequences each sampling period. The advantages and disadvantages of the proposed FS-MPC with the DSVM are analysed using a two-level three-phase inverter connected to the grid as setup to introduce the proposed technique. Simulation results are presented, showing that using the proposed technique the switching frequency is fixed and the sampling frequency can be lowered without reducing the quality of the converter behaviour.