In this paper, a new optimum fuzzy output quantity decision analysis of duopoly market is developed. To efficiently handle the fuzziness of decision variables, the linguistic values, subjectively represented by the triangular fuzzy numbers, are utilized to act as the evaluation tool of decision variables such as fixed cost and unit variable cost. This paper will apply fuzzy set theory to construct optimum output quantity decision model based on the goal of pursuit the maximum profits of duopoly market. This model can be applied to duopoly air passenger market, it can decide the optimum output quantity of per airline or per period based on thinking about output quantity of competitor. According to the optimum output quantity of per airline or per period, the airlines can make the decision of planning the optimum seats of aircrafts and optimum flights numbers.