This work is devoted to the admissibility analysis for singular time-delay systems by using delta operator approach. By estimating the delay term with a two-term approximation, the singular system in delta operator domain is transformed into an interconnection of a time-invariant subsystem with constant delay and a uncertain one. By resorting to the input-output approach, a delay-range-dependent admissibility criterion for the singular time-delay system in delta operator domain is obtained. By adding a triple-summation term to the Lyapunov-Krasovskii functional, the results are shown less conservative. Several examples are used to explicitly manifest the advantage of the given criterion.