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This paper considers the finite-time output feedback controller design for nonlinear discrete-time systems with time-delay and time-varying exogenous disturbances. The exogenous disturbances are unknown bounded signals. In this regard, a theorem is given and the sufficient conditions are extracted which guarantees the finite-time boundedness of the time-delay closed-loop system via selecting the appropriate Lyapunov-Krasovskii functional. Furthermore, the gain of output feedback is achieved through the feasibility testing of the derived linear matrix inequalities (LMIs). Finally, a numerical example is given to verify the effectiveness of the developed technique.