This paper addresses the tracking problem of leader-follower multi-agent systems subject to actuator saturation. A leader node or command generator is considered, which generates the desired tracking trajectory. To track such a leader, a new family of scheduled low-and-high-gain feedback controllers is designed for each follower, provided that the linear dynamic mode is asymptotically null controllable with bounded controls, and such control laws rely on the asymptotic property of a class of parametric algebraic Ricatti equations. We show that if the associated undirected graph of the system is connected, with the proposed control law, all the followers can track the leader eventually. A simulation example is finally given to illustrate the performance of the proposed control scheme.