This article is concerned with the problem of dissipativity and stability analysis for a class of neural networks (NNs) with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional (LKF), including some delay-product-type terms, is proposed, in which the information on time-varying delay and system states is taken into full consideration. Second, by employing a generalized free-matrix-based inequality and its simplified version to estimate the derivative of the proposed LKF, some improved delay-dependent conditions are derived to ensure that the considered NNs are strictly ( $Q$ , $S$ , $R$ )- $\gamma $ -dissipative. Furthermore, the obtained results are applied to passivity and stability analysis of delayed NNs. Finally, two numerical examples and a real-world problem in the quadruple tank process are carried out to illustrate the effectiveness of the proposed method.