The design of airfoil had practiced by repeat tests in its first stage, though an airfoil has as been designed based on simulations according to techniques of computational fluid dynamics. Here, using of traditional optimization is unsuitable because a state of flux is hypersensitive to the shape of airfoil. Therefore the paper optimized the shape of airfoil in transonic region using a genetic algorithm (GA). Response surfaces are based on back propagation neural network (BPN) and regression model. Training data of BPN and regression model were obtained by computational fluid dynamic analysis using CFD-ACE, and each analysis has been designed by design of experiments