This paper focuses on the fuzzy-H^∞-filter-design problem for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Two cases of the time-varying delays are considered: 1) The delays are differentiable and have both the lower and upper bounds of the delay derivatives, and 2) the delays are bounded but not necessary to be differentiable. Since we employ a new fuzzy Lyapunov-Krasovskii functional (LKF) and estimate a tighter upper bound of its derivative, the proposed delay-derivative-dependent bound-real-lemma (BRL) condition has advantages over some previous results in that it enlarges the application scope but has less conservatism, which is established theoretically. The BRL condition that depends on both the upper and lower bounds of the delay derivatives is derived. Then, based on the aforesaid BRL, a new fuzzy H^∞ filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear-matrix inequalities (LMIs). Finally, some numerical examples and an application to the truck-trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results.