Summary: A new method for the delay-dependent stability analysis for continuous-time Takagi-Sugeno (T-S) fuzzy systems with a time-varying delay is suggested, which is less conservative than other existing ones. Based on a Fuzzy Lyapunov-Krasovskii Functional (FLKF), a delay-dependent stability criterion is derived for the fuzzy systems. In the derivation process, some free-weighting matrices are introduced to express the relationships among the terms of the system equations, and among the terms in the Leibniz-Newton formula, which may avoid the conservation produced by some bounding inequalities for cross products between two vectors and model transformation. Finally, a simulation example shows that the approach is effective.