In this paper, the problem of delay-dependent robust stability for a class of linear uncertain systems with multiple time-varying delays is investigated. A new multiple time-varying delays criterion for improving the delay-dependent robust stability in the form linear matrix inequalities is proposed using the augmented Lyapunov-Krasovskii functional and Jensen's inequality. The result enlarges the existing maximum allowable bound of the time delay. Furthermore, we theoretically consider the relationship of the maximum allowable delay bound of each time-varying delay to reduce the conservatism. An illustrative example is given to show the efficacy of the obtained result.