Abstract: A type of optimal preview control problem for time-varying discrete-time systems with state time-delay is investigated.The methodology is to first construct an augmented error system by introducing a difference operator,and then transform the system into a traditional control system without time-delay in form by using the lifting technique to solve the problem that the operator is not a linear operator.Finally,preview information of the vector containing the desired tracking is introduced to obtain the ultimate augmented error system.Beginning with this augmented error system,a controller with a preview function which can process the original system is designed by making use of the results on optimal control for time-varying systems.Later,matrix partition is employed to transform the high-order Riccati equation that needs to be solved into a low-order Riccati equation.The effectiveness of the proposed design method is demonstrated by a numerical simulation.