In this technical note, we propose a model predictive tracking control algorithm for linear dynamical systems with input constraints. To achieve setpoint tracking, an integrator is inserted into the feedback loop. In the standard control strategy, integral action is used for all the time to remove steady state error. In the proposed control approach, the value of the integrator state is reset at each sampling time to improve tracking control performance until upper bound of the cost becomes sufficiently small. Then, the integral action is used to achieve offset-free tracking. The control algorithm is reduced to a convex optimization problem under linear matrix inequality constraints.