Min-Max MPC (MMMPC) controllers [P.J. Campo, M. Morari, Robust model predictive control, in: Proc. American Control Conference, June 10-12, 1987, pp. 1021-1026] suffer from a great computational burden which limits their applicability in the industry. Sometimes upper bounds of the worst possible case of a performance index have been used to reduce the computational burden. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound based on a diagonalization scheme. The upper bound call be computed with O(n(3)) operations and using only simple matrix operations. This implies that the algorithm can be coded easily even ill non-mathematical oriented programming languages such as those found ill industrial embedded control hardware. A simulation example is given in the paper. (c) 2005 Elsevier Ltd. All rights reserved.