This paper deals with the problem of robust fault detection for discrete-time switched systems with state delays under arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs and model uncertainties, the estimation error between the residuals and the faults is minimized. The problem of robust fault detection is converted into an H∞ filtering problem. By switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed method.