Designing high-performance and durable non-platinum catalysts as oxygen reduction reaction (ORR) catalysts is still a major barrier of fuel cell commercialization. In this work, simple hydrothermal and impregnation routes were applied to prepare non-platinum Pd-Co bimetallic nano-catalysts such as Fe-N doped graphene quantum dot (Fe-N-GQD) supported Pd3Co (Pd3Co/Fe-N-GQD 10 wt%), carbon supported Pd3Co/C (10 wt%), graphene quantum dot supported Pd3Co/C (10 wt%). The synthesized catalysts were physico-chemically characterized by X-ray diffraction (XRD), Raman spectroscopy, transmission electronmicroscopy (TEM), and X-ray photoelectron spectroscopy (XPS). The electrochemical investigation was carried out in three electrode half-cell system to evaluate the catalyst activity for oxygen reduction reaction (ORR), the tolerance to methanol crossover and durability. In comparison to commercial Pt/C (ETEK, 20 wt%), the Pd3Co/Fe-N-GQD with lower weight percentage catalyst (∼10 wt%) displayed comparable electrocatalytic activity toward ORR with even higher methanol-tolerance capability and durability. The fabricated Pd3Co/Fe-N-GQD with (10 wt %) metal loading exhibited only 20% lower activity than Pt/C (ETEK, 20 wt%) toward ORR. Nevertheless the durability study of the catalyst in acidic media showed that the Pd3Co/Fe-N-GQD preserve 40% of its activity while Pt/C (ETEK, 20 wt%) exhibited only 20% of its initial catalytic activity for ORR. Moreover the activity loss in the presence of methanol (0.1 M) was obtained for Pt/C (ETEK, 20 wt%) and Pd3Co/Fe-N-GQD 35% and 14%, respectively. To investigate the role of catalyst support, catalytic activities of Pd3Co/Fe-N-GQD, Pd3Co/C, Pd3Co/GQD and Pd/Fe-N-GQD were compared. The results demonstrated superior catalytic activity of Pd3Co/Fe-N-GQD which could be related to the cocatalytic role of Fe-N-GQD due to the presence numerous of active sites exposed to the reactants.