Based on the refined first-order shear theory (simplified zig-zag model), using quasi-conforming finite element method with path-following and switching approach, the postbuckling behaviors and postbuckling bearing capacity (PBC) of composite sandwich panels (CSPs) axially loaded were studied and discussed in detail. To utilize the carrying potential of CSPs in postbuckling, the effects of the key parameters on postbuckling behaviors of the CSPs were analyzed by finite element method. The numerical results show that the PBC of CSPs increases with the increase of face sheets thickness, core thickness and core shear modulus, but it is insensitive to the change of the side length ratio. The enhancement of core shear strength can increase the PBC of CSPs and change the failure mode, but it is found there is a threshold value, beyond which, the PBC will no longer or slightly increases with the increase of core shear strength. The failure of CSPs is mainly determined by the tensile strength in the direction perpendicular to the fiber. Finally, a parameter selection optimization approach is proposed to effectively improve the PBC of CSPs under axial compression.