Technologies of fuel cells and water electrolysis are promising in renewable energy for an eco-friendly environment. In particular, polymer electrolyte membrane fuel cell (PEMFC) has attracted attention because of their various advantages, however, the widespread of PEMFC is difficult due to scientific issues and economic problems of noble Pt. Therefore, it is very important to developing effective support materials of catalysts to enhance catalytic activity and durability. In water electrolysis, scalable electrocatalyst synthesis of active, durable, low-cost, and earth-abundant towards hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) remains a great challenge. In this thesis, we suggest strategies for developing durable PEMFC with heteroatom-doped graphene nanoribbons through the combination study of computational and experimental approaches. Additionally, we performed the DFT calculation to validate the reaction mechanism of electrocatalysts for water electrolysis. In Chapter 1, we selected graphene nanoribbons (GNR) as support materials because it has a large specific surface area and hydrophilic surface property, which is advantageous to the uniform dispersion of Pt nanoparticle (NP) on support materials. It has a lot of edge sites, which has benefits to doping heteroatoms for controlling properties of materials. However, abundant defect and edge sites of GNR can be a disadvantage because it would be an initial point of carbon corrosion. Based on studies of experiment and computational science, in this work, we employed fluorine as doping materials into GNR to overcome the carbon corrosion issue. In this study, we propose effective strategies to use F-doped GNR for developing durable PEMFC as supports and additives of Pt/C cathode. In Chapter 2, the Ni-Mo2C/NC@NF was developed experimentally as the bifunctional catalyst for the HER and OER with remarkable activity and stability in alkaline electrolyte. In this study, we employed DFT calculations to validate the surface reaction and the mechanism of electrocatalysts for HER and OER on prepared catalysts. DFT calculations were conducted three electrocatalysts to clearly understand the Ni doping effect in Mo2C/NC with electronic structural studies. The Gibbs free energies were calculated from the adsorption energy of atomic hydrogen (∆G(H*)) and oxygen intermediates (∆G(O*),∆G(OH* ),∆G(OOH* )) as a key descriptor for HER and OER. Therefore, results are unveiled why the Ni doping in Mo2C/NC lattice can improve catalytic activities for HER and OER by modifying the electronic structure of Mo2C/NC inconsistent with experimental results.