This paper deals with the problem of $H_{infty}$ fault detection for a kind of linear singular systems with time-varying delay. A generalized form of observer-based fault detection filter (FDF) is first used as a residual generator. Then the design of $H_{infty}$-FDF is formulated in the framework of $H_{infty}$ filtering. By applying Lyapunov-Kravoskii function approach, delay-dependent conditions on the existence of the $H_{infty}$-FDF, which ensure asymptotic stability and a prescribed $H_{infty}$ performance level, are derived. With the aid of a cone complementarity linearization technique, an iterative algorithm is proposed to calculate the parameter matrices of the $H_{infty}$-FDF in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed algorithm.