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Thin-walled structures, i.e. the wing-upper-skin panels, are prone to buckling accompanied by a significantly large out-of-plane deflection. The computational efficiency of the conventional finite element based full-order method is not satisfactory for nonlinear buckling problems of the structure. In this work, the skin panels on the upper surface of the wing butt box are selected using a sub-modeling technique based on the nonlinear structural analysis. A reduced-order method is proposed to trace the geometrically nonlinear response of the single and double-curved skin panels in a stepwise manner. A predictor-corrector strategy is developed using the Koiter-perturbation-theory based reduced-order model and Newton iterations. The high-efficiency of the proposed method is validated by comparing the number of path-following steps and iterations with the full-order method. A fairly large step size is achieved to significantly reduce the computational cost in a nonlinear buckling analysis. The influence of the number of closely-spaced modes on the numerical accuracy and efficiency of the proposed reduced-order method is also studied. Different boundary condition, location, and thickness of the wing-upper-skin panel, are considered to further demonstrate the favorable performance of the proposed method. • Nonlinear buckling analysis is applied to skin panels with single and double-curved shapes on the wing upper surface. • A reduced-order method is adopted to trace geometrically nonlinear responses in predictor-corrector based stepwise manner. • Influence of the number of closely-spaced modes on numerical accuracy and efficiency of the proposed method is investigated. • Numerical accuracy and high-efficiency of the proposed method are validated for skin panels con- sidering various parameters. [ABSTRACT FROM AUTHOR]