This paper proposes a robust fault detection and isolation (FDI) scheme for discrete time-delay system with disturbance. The FDI scheme can not only detect but also isolate the faults. The lifting method is exploited to transform the discrete time-delay system into the non-time-delay form. A generalized structured residual set is designed based on the unknown input observer (UIO). For each residual generator, one of the system input signals together with the corresponding actuator fault and the disturbance signals are treated as an unknown input term. The residual signals can not only be robust against the disturbance, but also be of the capacity to isolate the actuator faults. The proposed method has been verified by a numerical example.