An optimal preview controller based on the discrete-time H∞ control is presented. The preview controller is synthesized by considering the bounded unknown disturbances as well as pre-viewable commands and disturbances. The controller derivation procedure is analogous to the LQ-based scheme. The designed preview gain matrix has a similar structure as the LQ-based one. As the infinity norm γ of the transfer function matrix tends to ∞, the preview gains obtained by H∞ control method approach to the gains by the LQR. The LQ-based preview gains are verified to be subsets of the H∞-based preview gains.