Multi-level active neutral point clamped (ANPC) inverters are widely employed in industry due to their high voltage handling capacity, low current total harmonic distortion, and better power loss distribution among the power semiconductors. However, the existing control and modulation methods are mainly proposed for 3-level and 5-level ANPC inverters, leaving the relevant studies on 4-level ANPC inverter to be comparatively sparse. Moreover, complicated modulation schemes are usually needed for ANPC inverters with more than 3-levels due to the increasing challenge on capacitor voltage balancing. This paper presents a model predictive control approach for three-phase, 4-level ANPC inverter. The proposed approach produces superior control performance and well-balanced capacitor voltages while greatly simplifying the modulation process. Its validity is verified by experimental results.