The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper.The uncertainty is assumed to be norm-bounded.By establishing a finite sum inequality based on quadratic terms,a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs).A suitable robust state feedback control law is presented,which guarantees that the resultant closed-loop system is regular,causal and stable for all admissible uncertainties.Numerical examples are given to demonstrate the applicability of the proposed method.