This paper is concerned with the problem of robust stability of uncertain linear systems. The considered system has an interval time-varying delay and norm-bounded uncertainty. Based on a new Lyapunov-Krasovskii functional, which considers the fraction of both the lower and upper bounds of the interval time-varying delay, a delay-dependent criteria for robust stability is established in terms of strict linear matrix inequality (LMI). A numerical example illustrates the effectiveness of the approach and the improvement over previous methods.