In this paper, a composite anti-disturbance fault-tolerant controller is proposed for switched systems with multiple disturbances and actuator faults. The disturbances are divided into two parts: One is assumed to be a norm-bounded vector; the other part is generated by an exogenous system with parametric perturbations. First, a composite observer is constructed to estimate the disturbances described by an exogenous system and actuator fault simultaneously. Then, based on disturbance observer based control (DOBC), fault accommodation, and $L_2-L_\infty$ control, a composite anti-disturbance fault-tolerant controller is developed to reconfigure the considered systems with disturbance rejection and attenuation performance. By virtue of average dwell time method and Lyapunov function technique, the stability of the closed-loop system is analyzed. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control approach.