The problem of finite-time robust preview control is proposed for a class of uncertain discrete-time systems. It is different from the difference of error signal and system equation. By introducing auxiliary variables, we use the difference between the system state variables, input variables, and the corresponding auxiliary variables, instead of the usual difference between system states. This makes it possible to construct an augmented error system. In addition, the augmented error system derived no longer contains error vector, which not only reduces the order of the system, but also extends the applicable object. For the augmented error system, the state feedback and output feedback are introduced, receptively, and based on the Lyapunov stability theory, sufficient conditions are derived for the robust asymptotic stability of the closed-loop systems. The conditions can be realized by solving an LMI problem. The controller returns to the original system, the preview controller is obtained. The numerical simulation examples also illustrate the effectiveness of the results in the paper.