This paper considers the stability analysis problem for neural networks with time-varying delay. Firstly, the new augmented Lyapunov functional is constructed by employing the more general decomposition approach. Then based on the Lyapunov stability theory and free weight matrix method, the novel delay-dependent stability condition is derived in terms of linear matrix inequalities (LMIs). Numerical examples show that the proposed method is more effective than some existing ones. (C) 2009 Elsevier B.V. All rights reserved.