A delay-dependent approach to robust $H_{infty}$ filtering is proposed for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. The delays are interval time-varying delays and uncertainties are a convex compact set of polytopic types. The aim of the designed filter is to guarantee regular, causal, asymptotic stability with $H_{infty}$ norm bound of filtering error singular systems. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded lemma (BL) for singular systems with interval time-varying delays is proposed. Based on the result, the existence condition of the robust $H_{infty}$ filter and the filter design method are presented in terms of linear matrix inequality (LMI). Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.