This paper concerns the problem of robust fault detection filter design for uncertain linear time-invariant (LTI) systems with both model uncertainty and disturbances. Firstly, the fault detection filter design is formulated to $H_{infty}$ model-matching problem. Secondly, based on a new bounded real lemma, a sufficient condition for the existence of the robust fault detection filter is constructed in term of linear matrix inequalities (LMIs). Owing on the introduction of the tuning parameter and slack variables in obtained LMI condition, the proposed design method can provide higher fault detection sensitivity performance than the existing one. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed approach.