Curved composite panels are widely used in civil aircraft structures. Accurate prediction and understanding of their post-buckling behaviors are of great significance for ensuring structural safety and weight reduction. This study proposes an analytical solution for the post-buckling of cross-ply curved composite panels based on a double trigonometric series, which accounts for the effects of initial geometric imperfections and the phenomenon of crest shift. The nonlinear relationship between compressive load and deflection are derived using the Galerkin’s method. Experiment specimens of curved composite panels with dimensionless curvatures ranging from 10.0 to 15.0 are fabricated using T300/EPW carbon fiber prepreg. The analytical prediction method proposed in this study is calibrated and optimized through post-buckling compression tests and particle swarm optimization algorithms, demonstrating an overall error of less than 7%.