A nano-structured carbon material referred to as Graphene-Carbon Nanotube hybrid is developed for electrochemical energy conversion and storage devices. The hybrid is obtained by catalyst-free growth of free-standing graphene on CNT scaffolds. The hybrid combines the advantageous properties of constituent materials, including an ultra-high density of graphitic edges of graphene and a porous structure of CNTs. As a catalyst support for platinum in PEM fuel cells, the hybrid shows both enhanced catalytic activity and superior stability compared to a commercial carbon black-supported platinum catalyst. The hybrid is also used as a support material for amorphous molybdenum sulfide in supercapacitor and hydrogen evolution reaction catalyst applications. As a supercapacitor electrode material, the hybrid shows high specific capacitance and good stability. As a hydrogen evolution reaction catalyst, the hybrid is one of the most active non-precious catalysts ever reported. FIB-SEM tomography is used to reconstruct the porous 3D structure of carbon electrodes.