The class of preview control problems of discrete-time linear systems with both state delay and input delay are studied. Discrete lifting technology and variable substitution method are applied to eliminate the state delay and input delay respectively, thus a delay-free system is obtained. On this basis, the preview control theory and the state predictor method are used to acquire a preview controller which is equipped with state delay's compensation, input delay's compensation and reference signal's preview compensation. Different time delays are eliminated by utilizing different methods, which can reduce the dimension of the augmented system effectively. Finally, a numerical example is given to show the effectiveness of the design method.