The aim of this paper is to study the problem of asymptotic stability analysis for T-S fuzzy neural networks with discrete interval and distributed time-varying delays by employing a further improved free-weighting matrix approach. Based on the new Lyapunov-Krasovskii functional with triple-integral term, using some integral inequality and convex combination technique, a new delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs) that can be checked easily by the LMI Control Toolbox in MATLAB. Finally, numerical examples are given to illustrate the strength of the proposed method and an improvement over some existing results. © 2012 Springer-Verlag London Limited.