Proton Exchange Membrane Fuel Cells (PEMFCs) are electrochemical devicesrnthat convert chemical energy into electricity. Due to their higher energy conversionrnefficiency and lower emission of pollutants, they are a promising alternativernpower supply for future automobile applications. However, the sluggishrnkinetics of the Oxygen Reduction Reaction (ORR) at the cathode and rarernand expensive platinum based catalysts are the major problems that hinderedrnthe widespread commercialization of fuel cells. There are two main strategiesrnto solve these problem: (i) decrease the amount of platinum content e.g., byrnalloying Pt with other metals; (ii) use a non-precious catalyst made of earthabundantrnelements. In this thesis, both possibility are investigated computationallyrnusing Density Functional Theory. In the fist work, the ORR activity ofrnPt-skin Pt3V(111) catalyst was investigated. The results revealed that the ORRrnintermediates (*O, *OH and *OOH) have lower binding energies on Pt-skinrnPt3V(111) compared to pure Pt(111) surface. The ORR on Pt-skin Pt3V(111)rnsurface proceed via *OOH dissociation with an activation energy of 0.33 eV.rnMoreover, the DFT results revealed that the negative formation energy of thernPt3V alloy and the positive dissolution potential shift of the surface Pt atomsrnrevealed the better stability of Pt-skin Pt3V(111) surface over pristine Pt(111)rnsurface. Due to the comparable activity and better stability, the new Pt-skinrnPt3V(111) alloy electrocatalyst is promising for the development of low-costrnand efficient PEMFCs. Secondly, the ORR activity of graphene based catalystsrnsuch as graphene (G), single vacancy defective graphene (GSV), Quaternary Ndopedrngraphene (NGQ), and pyridinic N-doped graphene (NGpy, 3NGpy, andrn4NGpy) on Co(0001) substrate was studied. The results show pyridinic N-dopedrngraphene on Co support Co/3NGpy exhibited better performance than the NGQrnon Co support and free-standing systems. The overpotential for Co/3NGpy isrnrather higher compared to pure Pt(111) catalyst (0.65 V). Therefore, pyridinicrnN-doped graphene with cobalt support could be a promising strategy to enhancernthe ORR activity of N-doped graphene in PEMFCs. Finally, the ORR catalyticrnactivities of Co-Nxâˆ’4Sx/C single atom catalysts (SACs) are studied. The DFTrnresults revealed that the adsorption energy of the *OH intermediate bound onrnCo-N3S/C, Co-N2S2/C, Co-N3S/C, and Co-S4/C is weaker than that of thernCo-N4/C catalyst. The results show that Co-N3S/C catalyst revealed the lowerrnoverpotential (0.37 V) than Co-N4/C (0.57 V). Slightly less amount of chargesrnare transferred from Co atom in Co-N3S/C to ORR intermediates as comparedrnto Co-N4/C and the d-band center of Co atom changes from -0.71 eV (Co-N4/C)rnto -0.91 eV (Co-N3S/C). This explains the weaker adsorption energy of *OHrnon Co-N3S/C catalyst. Therefore, Co-N3S/C is a promising non-precious singlernatom catalyst for an efficient ORR activity in acidic solution in fuel cell.