Abstract: Robust design optimization has gained increasing concern in the engineering design process because it can provide an economical design that is insensitive to variations in the input variables without eliminating their causes. The key of robust design is uncertainty analysis. So in this paper the uncertainty analysis based on polynomial chaos was investigated and combined with CFD method to quantify the uncertainties in computational aerodynamic design. The transonic flow around RAE2822 airfoil is studied to test the presented method and analyze the effect of the polynomial order to the precision of the aerodynamic characteristic. The robust design of a supercritical airfoil based on the uncertainty of Mach number was conducted to validate the PCE method. It is shown by the optimization result that the drag coefficient was decreased at the design point while the sensitivity of the drag coefficient about the Mach number was weakened. It is proved that the PCE method can improve the efficiency of robust design and is a good choice for aerodynamic robust design.