Based on the parameter-dependent Lyapunov function method and the LMI technique, the problem of finite-time output feedback preview control is proposed for a class of polytopic uncertain discrete-time systems. Firstly, the difference operator is introduced, the discrete lifting technology is employed, and an augmented error system including previewed information is constructed by using the error system method in preview control theory, which leads to a finite-time preview control problem being transformed into a finite time stabilization problem. Then, the previewable signals are fully utilized through reformulation of the output equation, considering the output feedback for the augmented error system, the condition of finite-time stability of closed-loop system and the design method of preview controller are given by LMI technique. Research result shows that the static output preview controller parameter matrices can be achieved from the solution of LMIs problems. The numerical simulation examples illustrate the validity of the proposed method in this paper.