Abstract: Geometry optimization and calculation about the band structure of the three-dimensional composite, consisting of porous single layer graphene covalently bonded with single-walled carbon nanotubes, are studied in this paper. The connections between graphene and carbon nanotubes are verified to be covalent bond. The elastic constant and deformation potential constant of single-layer graphene-nanotube composite are calculated in deformation potential theory. Its noted that the carrier mobility is about 104 cm2/(Vs) for both electrons and holes. It is about one order of magnitude lower than that of graphene. This composite structure has great future in organic electronics because of its possible extension to three-dimension.