In this study, we investigate the efficiency of gradual design optimization that uses the degree elevation property of Bezier curves. Thanks to the degree elevation property, airfoil shapes can be defined by any numbers of control points (design variables). By using this property, the number of design variables can be increased during the design optimization process. A gradual design optimization approach is developed with a downhill simplex method It was confirmed that the developed approach increased not only the efficiency but also the stability of design optimization.