Uncertainties will make aircraft deviate from the designed condition, resulting in the decrease in aerodynamic performance and even destruction. This paper presents a fast nonlinear interval analysis method considering geometric uncertainties. DFFD method is used to parameterize the airfoil shape, and the Kriging model for aerodynamic force and uncertainty variables is optimized by PSO algorithm to find the upper and lower bounds of the objective interval. The effects of geometric uncertainties on NACA0012 airfoil are analyzed using the above method. And then, a robust optimization design method is established based on the interval analysis method. FFD method is used to produce the deterministic design variables and the order relation of interval number is employed to transform the uncertain optimization to deterministic multi-objective optimization which is solved by MOPSO based on Pareto entropy. The robust optimization design is implemented for the symmetrical airfoil with the drag objective under geometric uncertainties and thickness constraint, and the results are compared with the deterministic optimization to validate the effectiveness of the developed method.