In this paper, we present a wavelet multiresolution model based adaptive model predictive control strategy for control of unknown nonlinear systems subject to input and state constraints. The wavelet multiresolution analysis framework is used as the building block to approximate the unknown nonlinear system dynamics by virtue of the promising function approximation capability of wavelet networks. The parameter estimation routine employed guarantees non-increase of the prediction error vector. The identified wavelet network nominal model is then combined within nonlinear model predictive control framework to address the adaptive constrained MPC problem. The asymptotical stability of the proposed adaptive MPC technique has been proved using Lyapunov stability theorem with terminal cost and terminal constraint. An illustrative example on the choice of the stabilizing design parameters to ensure satisfaction of stability condition is provided.