In this technical note, an adaptive model predictive control (MPC) is proposed for unconstrained discrete-time linear systems with parametric uncertainties. The control objective is reference tracking. The adaptive MPC is designed by combining an adaptive updating law for estimated parameters and a constrained MPC for an estimated system. It is proved theoretically that, with the proposed adaptive MPC, the closed-loop system is capable of tracking time-varying reference signals with ultimately bounded tracking errors, and the estimated parameters are bounded. Moreover, if the reference signals are constant, tracking errors of the closed-loop system can be stabilized asymptotically. Performances of the closed-loop system are demonstrated by a simulation example.