This paper is concerned with a new Lyapunov-Krasovskii functional (LKF) approach to the stability for neural networks with time-varying delays. The LKF has two features: First, it can make full use of the information of the activation function. Second, it employs the information of the maximal delayed state as well as the instant state and the delayed state. When estimating the derivative of the LKF we employ a new technique that has two characteristics: One is that Wirtinger-based integral inequality and an extended reciprocally convex inequality are jointly employed; the other is that the information of the activation function is used as much as we can. Based on Lyapunov stability theory, a new stability result is obtained. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones.