In this research, a numerical study has been provided for examining the nonlinear stability behaviors of sandwich beams having a cellular core and two face sheets made of nanocomposites. The nonlinear stability behaviors of the sandwich beam having geometrically perfect/imperfect shapes have been studied when it is subjected to a compressive buckling load. The nanocomposite face sheets are made of epoxy reinforced by graphene oxide powders (GOPs). Also, the core has the shape of a honeycomb with regular configuration. Using finite element method based on a higher-order deformation beam element, the system of equations of motions have been solved to derive the stability curves. Several parameters such as face sheet thickness, core wall thickness, graphene oxide amount and boundary conditions have remarkable influences on stability curves of geometrically perfect/imperfect sandwich beams.