Abstract: Up to date, the Kriging-based optimization methods are widely used in the aerodynamic optimization design, however, it hasn’t been successfully applied to the aerodynamic inverse design problems. In this research, the Kriging-based optimization method is applied to the single and multi-point airfoil inverse design, and its feasibility to inverse design problems is validated; besides, the choice of infill criteria is investigated. Moreover, this method is compared to the polynomial response surface based method (P-RSM) and the Adjoint-based method, the results show that the Kriging-based method outperforms the P-RSM, and has comparable efficiency with Adjoint-based method but better flexibility and easier to use. Finally, the current method is applied to engineering inverse airfoil design problems and its feasibility is validated.