The design problem of an optimal deadbeat state observer for discrete-time systems has been discussed in this paper. The non-measurable states of the plant are reconstructed with a reduced-order dynamic observer. The problem of estimation is treated as a regulator problem wherein the quadratic performance index, which penalizes the error in estimation, is minimized in an average sense over a set of observer gain matrices which force observer poles to the origin. An efficient computational procedure based on direct cost optimization using gradient type algorithm is also reported. A case study of a boiling water reactor power plant has been presented to illustrate the usefulness of the proposed optimal deadbeat observer.