Abstract: Airfoil geometry stochastic uncertainty has a great effect on aerodynamic performance. The effect of an airfoil geometry uncertain fluctuation on aerodynamic characteristics is discussed and a robust design is performed to reduce this effect. Class-shape function transformation (CST) method is employed, which can greatly reduce the number of design variable freedoms. NACA0012 airfoil is carried out to analyze the probabilistic uncertainty, the result indicate that the tiny fluctuations of the geometry have little effect on the lift characteristics. The paper develops a robust optimization design based on a response surface method and genetic algorithm. The robust design can largely reduce the drag fluctuations and improve computational efficiency. Comparing to deterministic optimization, the robust optimization make the drag increase slightly but the fluctuations decrease largely, the aerodynamic performance have better robustness.