The delay-dependent robust stability problem for uncertain neutral system with mixed time-varying delays is studied. The whole delay interval is partitioned into two equidistant subintervals at its central point and a new Lyapunov-Krasovskii(L-K) which contains some triple-integral terms and augment terms are introduced on these intervals. Then, by using the L-K stability theorem, the integral inequalities method together with the free weighting matrix approach, a neutral and discrete delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities(LMIs). Finally, the simulation results show that the proposed criterion improves some exist results and have less conservatism.