This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional together with a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities ( LMIs) . Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.