This paper considers an infinite-horizon min-max model predictive control (MPC) problem for time-delay discrete systems with a polytopic uncertainty description, which has rarely been addressed in the literature. Several new solutions to this problem are proposed which are inter-complementary. If there is an input delay, then the single state feedback solution requires all the system matrices to be stable. This deficiency can be removed by adding free control moves before a modified state feedback law. If there is no input delay, then a computationally efficient off-line state feedback solution can be applied. In order to obtain desirable region of attraction while at the same time preserve reasonably low on-line computational effort, one can choose the standard solution. Simulation results are given to illustrate these new solutions.