Graphene and single-walled carbon nanotubes are carbon materials that exhibit excellent electrical conductivities and large specific surface areas. Theoretical work suggested that a covalently bonded graphene/single-walled carbon nanotube hybrid material would extend those properties to three dimensions, and be useful in energy storage and nanoelectronic technologies. Here we disclose a method to bond graphene and single-walled carbon nanotubes seamlessly during the growth stage. The hybrid material exhibits a surface area >2,000 m(2) g(-1) with ohmic contact from the vertically aligned single-walled carbon nanotubes to the graphene. Using aberration-corrected scanning transmission electron microscopy, we observed the covalent transformation of sp(2) carbon between the planar graphene and the single-walled carbon nanotubes at the atomic resolution level. These findings provide a new benchmark for understanding the three-dimensional graphene/single-walled carbon nanotube-conjoined materials.