The optimal preview control problem is proposed for discrete-time descriptor causal systems in a multirate setting. First, according to the characteristics of causal systems, the descriptor system is transformed into an algebraic equation and a normal system represented by a dynamic equation. Second, by using the discrete lifting technique, the normal multirate system is converted to a single-rate system. Then by making use of the standard linear qudratic (LQ) preview control method, we construct the augmented error system, and the optimal preview control law of the augmented error system is obtained. The control law for the augmented system is then transformed to the optimal preview control law of the descriptor causal system in a multirate setting. The stabilisability and detectability of the lifted single-rate system and the augmented error system are discussed in detail. The effectiveness of the proposed method is shown by simulation.