The problems of robust delay-dependent stability and dissipativity for neural networks(NNs) with time-varying delay is investigated. A proper augmented Lyapunov-Krasovskii functional(LKF) is constructed, which fully utilizes the information of time-delay in integral term and the neuron activation function conditions. Then, by employing the free-matrix-based integral inequality to handle the derivative of the LKF, a less conservative delay-dependent stability criteria is obtained. The acquired conclusion is extended to the analysis of dissipativity for delayed NNs, and a suficient condition is derived to guarantee the NNs strictly$(\mathcalX, \mathcalY, \mathcalZ)-\gamma$-dissipative. The superiority and feasibility of presented approaches are verified via three numerical examples.