Neutral time delay system is a special system which has wide application in prac-tical systems. In this paper, we consider the delay-dependent robust stability problem for neutral system with mixed time-varying delays and nonlinear perturbation. Based on the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional with triple integral terms involving lower and upper bounds of interval time-varying delays is constructed for the system. Then, combined with the integral inequalities method, the free weighting matrix approach and the convex combination technique, a neutral and discrete delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities (LMIs). Finally, the numerical examples are presented to illustrate the effectiveness and improvement over some existing results in the literature with the proposed results.