Abstract: The delay-dependent robust stability problem is investigated for a class of systems with interval time-varying delay under nonlinear perturbations. Based on the delay central point method, the whole delay interval is divided into two equidistant subintervals at its central point, and a new Lyapunov-Krasovskii (L-K) functional with triple-integral and augment terms involving the central point information is introduced on these intervals. Combined with the L-K stability theorem, the integral inequality method, and the free weighting matrix approach, a new delay-dependent stability criterion is formulated in terms of linear matrix inequality (LMI). Finally, numerical examples are included to show that the proposed method is effective and can provide less conservative results.