An analysis has been made of the stability of T-S fuzzy systems with a time-varying delay. Firstly, by using the line integral Lyapunov function as well as the augmented Lyapunov functional method, a Lyapunov functional with more effective information is constructed, so as to make it possible that the augmented vector includes not only double integrals, but also time-delay product double integrals. Secondly, a generalized free weight matrix inequality method with a higher estimation accuracy is adopted to define the integral term in the functional derivative, thus obtaining a less conservative stability criterion. Then, the stability conditions are transformed into linear matrix inequalities by the third order matrix inequalities. Finally, a verification of the advantages of the proposed stability criterion can be achieved by providing two numerical examples.