Abstract: Based on theories of multi-objective decision making and fuzzy game,the multi-objective two-person zero-sum matrix game,whose payoff value is a vague value is studied.Two solution methods regarding vague multi-objective two-person zero-sum matrix game are discussed: one is making the vague multi-objective game problem certain through the order function of vague values first,then turning it into single objective game;the other method is turning vague multi-objective game problem into vague single objective game problem first,then making it certain through the order function of vague values.Numerical examples show that both methods can easily reach at equilibrium strategy and equilibrium solution.