This paper investigates robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty Under consideration includes polytopic-type uncertainty and linear fractional norm-bounded Uncertainty. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to drive some new delay-dependent stability criteria. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no redundant matrix variable is introduced. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria. (c) 2008 Elsevier Ltd. All rights reserved.