Abstract The problem of stability analysis of Takagi-Sugeno(T-S) fuzzy systems with time-varying delays is investigated in this paper. First, an extended delay-dependent reciprocally convex inequality containing some existing reciprocally convex inequalities is given. Second, a suitable augmented Lyapunov-Krasovskii functional (LKF) is proposed by introducing some new integral vectors ∫ t - h 1 t x v dv - x ( u ) , ∫ t - h 2 t - h 1 x v dv - x ( u ) , and several pairs of s-dependent integral vectors. Third, the improved stability criteria for T-S fuzzy systems are derived. Finally, several numerical examples are given to illustrate advantages and effectiveness of the proposed criteria by comparing the maximum delay bounds.