Abstract: A design method of H_∞ optimal guaranteed performance preview controllers was investigated for a class of polytopic uncertain discrete system with time-delay and constant parameters. First,different from the previous approaches,in order to keep the dimension of the state vector in the augmented error system from increasing with the addition of time-delay,the time-delay terms were maintained in that system. Then,a memory state feedback controller was designed for the augmented error system. The existence condition and the design method of the controller were obtained by the linear matrix inequality(LMI) method. At last,by solving an optimization problem with LMI constraint conditions,the H_∞ optimal guaranteed performance controller,which was the H_∞ guaranteed performance preview controller to the original system,was gained.