This paper presents a control method for a four-leg three-level flying capacitor converter (FCC) operating as a shunt active power filter (SAPF), based on model predictive control with finite number of control states (FS-MPC). Current control and capacitor voltage balancing are described. Influence of the mismatch of the inductive filter model parameters on the current control precision is analysed. Results are supported by the experimental waveforms obtained with a 10kVA set-up.