This paper presents a min-max generalized predictive control (MMGPC) which is robust to disturbances and has guaranteed stability. The MMGPC is derived from the min-max problem. It has non-recursive forms which do not use the Riccati equations. Stability conditions of the proposed control law are presented, which can be met by adjustment of some parameters such as input-output weightings. This paper presents a systematic way to obtain appropriate parameters for these stability conditions by using the linear matrix inequality (LMI) method. It is also shown that the suggested control guarantees that induced norm from disturbances to system outputs is bounded by a constant value under the same stability conditions.