The problem of H_∞ output feedback for uncertain linear discrete-time systems with state-delay and parameter uncertainties is considered. The objective is to design a linear output feedback controller such that, for the unknown state time-delay and all admissible norm-bounded parameter uncertainties, the feedback system remains robustly stable and the transfer function from the exogenous disturbances to the state-error outputs meets the prescribed H_∞ norm upper-bound constraint. The delay-independent output feedback does not depend on the uncertainties. The conditions for the existence of the robust H_∞ output feedback controller and its analytical expression is then characterized in terms of Riccati-type equations.