This paper concerns with the problem of stability analysis for the delay-dependent systems with nonlinear perturbations. In order to obtain a new less conservative stability criteria, the augmented form of Lyapunov-Krasovskii functional is constructed based on refined Jensen-based inequality, Wirtinger-based double integral inequality and improved reciprocally convex approach. Numerical example is given to demonstrate the effectiveness of the proposed method. Compared with some existing results, the results we obtained have less conservativeness and better robustness.