The aim of this paper is to design a nonlinear model predictive control for DC-DC buck converters to track constant reference signals with zero steady-state error. The online trained neural network (NN) model is employed as the predictor and the steady-state error, which is called the offset, is studied in the presence of the changes in system parameters and the external disturbances. The stability of the closed-loop system is investigated using the Lyapunov direct theory. The proposed method can provide offset-free behavior in the presence of constant disturbances. For rejecting nonconstant disturbances, a nonlinear disturbance observer based on the NN inverse model is proposed. Due to wide applications of the DC-DC converter in power electronics, control of its output voltage is considered in this paper. The effectiveness of the proposed control method is demonstrated by experimental results.