A method for making a graphene/carbon nanotube composite structure includes providing a metal substrate including a first surface and a second surface opposite to the first surface, growing a graphene film on the first surface of the metal substrate by a CVD method, providing at least one carbon nanotube film structure on the graphene film, and combining the at least one carbon nanotube film structure with the graphene film, coating a polymer layer on the at least one carbon nanotube film structure, and combining the polymer layer with the at least one carbon nanotube film structure and the graphene film, and forming a plurality of stripped electrodes by etching the metal substrate from the second surface.