This paper deals with the problem of *H∞ *fault estimation for linear time-delay systems in finite frequency domain. First a generalized coordinate change is applied to the original system such that in the new coordinates all the time-delay terms are injected by the system’s input and output. Then an observer-based *H∞ *fault estimator with input and output injections is proposed for fault estimation with known frequency range. With the aid of Generalized Kalman-Yakubovich-Popov lemma, sufficient conditions on the existence of the *H∞ *fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.