In view of the characteristics of the fuzzy nature of real economic management decision making environment and conditions, this paper studies a class of cooperative games that the values of coalitions are expressed with trapezoidal fuzzy numbers. The main purpose of this paper is to develop a kind of least square optimization method for solving trapezoidal fuzzy number cooperative games. Firstly, according to the concept of the trapezoidal fuzzy numbers' distance(square) and the least square method, an optimized mathematical model is proposed by considering that players in coalitions try to guarantee their payoffs' sums being as close to the coalitions' values as possible. Then all players' analytical formulas of trapezoidal fuzzy number payoffs are determined by the optimized mathematical model. Finally, some important properties of the least square solutions are discussed.The new model is proposed to avoid the uncertainty expansion caused by the trapezoidal fuzzy number subtraction, which can provide a new theoretical perspective and practical tool for solving the trapezoidal fuzzy number cooperative games.