This paper considers the problem of exponential stability for continuous-time singular systems with interval time-varying delay. By defining a novel Lyapunov-Krasovskii function and giving a tighter upper bound of its derivative, a new delay-range-dependent exponential admissibility criterion, which not only guarantees the regularity, absence of impulses and exponential stability of the system but also gives the estimates of decay rate and decay coefficient, is established in terms of linear matrix inequality (LMI). The resulting criterion has advantages over the result previously reported by Haidar et al. [17] in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Examples are provided to demonstrate the advantage of the proposed criterion.