NOVELTY - The method comprises associating a graphene film with a substrate, applying a catalyst and a carbon source to the graphene film, and growing carbon nanotubes on the graphene film, where the grown carbon nanotubes are covalently linked to the graphene film through carbon-carbon bonds, the grown carbon-carbon bonds are junctions between the carbon nanotubes and the graphene film, and the grown carbon nanotubes are in ohmic contact with the graphene film through the carbon-carbon bonds the junctions. The associating step comprises forming the graphene film on the substrate.    USE - The method is useful for making a graphene-carbon nanotube hybrid material (claimed) that is useful in electrical devices such as two-electrode electric double-layer capacitors, field emitter devices, dampeners, batteries, photovoltaic devices and fuel cells.    ADVANTAGE - The method is capable of effectively making the graphene-carbon nanotube hybrid material with good structural integrity and electrical properties thus improving performance and electrochemical properties of the electrical devices.    DETAILED DESCRIPTION - The method comprises associating a graphene film with a substrate, applying a catalyst and a carbon source to the graphene film, and growing carbon nanotubes on the graphene film, where the grown carbon nanotubes are covalently linked to the graphene film through carbon-carbon bonds, the grown carbon-carbon bonds are junctions between the carbon nanotubes and the graphene film, and the grown carbon nanotubes are in ohmic contact with the graphene film through the carbon-carbon bonds the junctions. The substrate is a copper foil and a porous substrate. The associating step comprises forming the graphene film on the substrate and transferring a pre-grown graphene film onto the substrate. The forming step comprises chemical vapor deposition. The catalyst comprises a metal and a buffer. The buffer has a thickness of 1-10 nm. The metal has a thickness of 1 nm. The applying step comprises: depositing the metal onto a surface of the graphene film; and depositing the buffer onto a surface of the metal. The applying step occurs by electron beam deposition. The growing step comprises heating at temperatures of 500-1100 degrees C. The catalyst is lifted off from the graphene film by the carbon nanotubes. The grown carbon nanotubes comprise vertically aligned carbon nanotubes that are perpendicular to the graphene film; and removing the substrate from the graphene-carbon nanotube hybrid material, where the removing step forms free-standing graphenecarbon nanotube hybrid materials. The method further comprises controlling a length of the grown carbon nanotubes. The controlling step comprises adjusting carbon nanotube growth time. A growth time is adjusted to 1-20 minutes. The removing comprises etching the substrate from the graphene-carbon nanotube hybrid material. The graphene-carbon nanotube hybrid material spans a side of the substrate and both sides of the substrate. The junctions comprise seven-membered carbon rings. The junctions are seamless. An INDEPENDENT CLAIM is included for a graphene-carbon nanotube hybrid material.