This paper proposes an advanced model predictive control for the three-level active-neutral-point-clamp (ANPC) inverter in order to improve the system performance with fast dynamic response and ensure the stability of the controller. The proposed scheme is Lyapunov function based voltage mode control which utilizes the discrete behavior of the converter considering the unavoidable quantization errors between the controller and the control actions selected from the finite control set of the ANPC inverter. A three-level three-phase ANPC inverter model is developed in MATLAB/Simulink environment to verify the effectiveness of the proposed MPC scheme. The simulation results confirm the computational speed improvements of the proposed MPC algorithm without compromising the performance such as total harmonic distortion (THD) of the three-level ANPC inverter. Moreover, the stability of the proposed technique is ensured by the nonlinear system model. Furthermore, the dc-link capacitor voltage balancing is also accurately maintained by the proposed controller at all times.