This paper studies the time-varying formation tracking problem for general linear multi-agent systems with multiple leaders in the presence of both actuator failure and input saturation. The followers are required to uniquely determine and track the convex combination of the states of leaders, while maintaining a predefined time-varying formation. A hyperbolic tangent function is firstly introduced to modify the actuator model with input saturation constraint. Then, an augmented plant for dynamics of each follower is constructed to derive the control protocol by exploiting the dynamic surface control technique. The proposed control protocol deals with faults of bias and unknown bounded loss of effectiveness by means of adaptive fault-tolerant strategies, while a formation feasible condition should be satisfied. With the control signal generated by the augmented plant, the time-varying formation error is proved to be semi-globally uniformly bounded under the faults and input saturation, based on standard Lyapunov theory. Finally, a numerical simulation is implemented to demonstrate the effectiveness of the proposed algorithm.