A simple genetic algorithm(SGA) is modified to form self-adaptive genetic algorithm(SAGA) in aerodynamic optimization design. Real number coding skill is used in the algorithm to represent individuals of population, while binary coding and encoding are not required. In order to improve the quality and efficiency of optimization design, crossover and mutation operators are designed with respect to specified problem. Then self-adaptive genetic algorithm is adopted to maximize lift-to-drag ratio of transonic airfoil and wing as examples. Analysis approves the designed results reasonable.