This paper concerns a problem of robust stabilization of a class of discrete-time systems with norm-bounded parameter uncertainty and unknown constant delay. A new delay-dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities. An algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties. numerical examples are given to illustrate the proposed results.