In this paper, a novel adaptive model predictive control (MPC) strategy is proposed for controlling a discrete-time multi-input multi-output (MIMO) linear system with constant uncertain parameters and subjected to input constraints. An adaptive law, designed to update the estimated parameters of the plant, is combined with a MPC algorithm for the estimated system. A normalizing factor is introduced in the adaptive update law, that removes its dependency on the bounds of the regressor vector as well as on the rate of adaptation gain. The proposed adaptive law guarantees stability of the parameter estimation error. The state estimation errors are proved to be bounded and asymptotically converging to zero. Stability analysis of the closed-loop system with the proposed adaptive MPC strategy is proved to show the boundedness and asymptotic convergence of the tracking error to zero.