In this paper, we propose a design method of a dual-mode model predictive control law for linear dynamical systems with input constraints. The proposed control law is composed of a finite horizon open-loop optimal control law and a state-dependent gain-scheduled feedback control law. By using the proposed control law, both high control performance and large region of attraction ca be achieved. We show that, by using the control law, the closed-loop stability can be guaranteed and the tracking error converges to zero in the case where a reference signal to be tracked is generated by a certain linear dynamics. The control algorithm is reduced to a convex optimization problem under linear matrix inequlitity constraints.