A study has been conducted on the stability of T-S fuzzy system with time-varying delays. Based on Lyapunov-Krasovskii (L-K) stability theory, a new augmented L-K functional can be constructed. By using the second-order Bessel-Legendre inequality with formal variation, an analysis has been made of the stability of T-S fuzzy system with time-varying delays with the extended inverse convex matrix method adopted and the constant-zero equation introduced, thus obtaining a less conservative stability criterion. Two numerical examples illustrate the effectiveness and feasibility of the proposed method.