In this note we consider the problem of H-infinity observer design for a class of uncertain linear discrete-time systems with delayed state and parameter uncertainties. The goal of this problem is to design a linear state observer such that, for the positive integer state time-delay and all admissible norm-bounded parameter uncertainties, the observation process remains robustly stable and the transfer function from exogenous disturbances to error stale outputs meets the prespecified H-infinity-norm upper-bound constraint. The observer structure does not depend on the parameter uncertainties. A simple, effective algebraic methodology is developed to derive the conditions for the existence of the desired robust H-infinity observers, and the analytical expression of these observers is then characterized in terms of the matrix Riccati-like equations/inequalities. We provide a numerical example to demonstrate the validity and the applicability of the proposed approach.