The present work aims to investigate the buckling performance of sandwich structure of functionally graded carbon nanotube-reinforced composite (FG‐CNTRC). Through first-order shear deformation theory, an analytical model for the sandwich structure of FG‐CNTRC was established. The governing equation for the prediction of the buckling performance of the sandwich structure of FG‐CNTRC was obtained through energy method. There was analytical solution that can satisfy both boundary conditions. The theoretical model and method were verified by literature analysis, and the influence of each parameter on the buckling performance was evaluated and performed on the basis of the corroborated model. The findings can lay a solid foundation of the design and application of the sandwich structure of FG‐CNTRC.