The definition of a matrix game with payoffs of interval-valued intuitionistic fuzzy sets(IVIF-sets) and the concept
of its solutions are given. The maximin and minimax strategies of two players can be obtained by solving a pair of primaldual linear programming models derived from two auxiliary nonlinear multi-objective programming models. A numerical example shows that the proposed method is effective and practical. The concept and methodology of matrix games with payoffs of IVIF-sets are not only an extension of those of classical matrix games, but also provide a new route for solving matrix games with interval-valued intuitionistic fuzzy information.