Abstract: A state observer with preview information for linear discrete-time systems was studied and applied to preview control systems. To design the state observer, an augmented error system with previewable desired tracking and disturbance signals was derived first, which leads to obtaining an optimal preview controller. While in designing the state observer, previewable desired tracking and disturbance signals were fully utilized through reformulation of the output equation. The state observer is a full-order dimensional observer with respect to the original system;whereas it is a reduced-order observer with respect to the augmented error system. Numerical simulation verifies the effectiveness of the state observer.