This paper investigates the problem of fault detection filter design for discrete-time switched systems with interval time-varying delays. The residual generator is constructed based on a mode-dependent fault detection filter, i.e., the designed fault detection filter is also a switched system as well. By constructing a novel switched Lyapunov functional, a new criterion is obtained for the residual system. Based on this, a sufficient condition for the existence of the above filter is established in terms of linear matrix inequalities (LMIs). The designed fault detection filter can guarantee the difference between the generated residual signal and the fault signal as small as possible. An example is provided to illustrate the effectiveness of the proposed method.