Novel Cu-nitrogen doped graphene nanocomposite catalysts are developed to investigate the Cu-nitrogen doped fuel cell cathode catalyst. Density functional theory calculations are performed using Gaussian 09w software to study the oxygen reduction reaction (ORR) on Cu-nitrogen doped graphene nanocomposite cathode catalyst in low-temperature fuel cells. Three different nanocomposite structures Cu2–N6/Gr, Cu2–N8/Gr and Cu–N4/Gr were considered in the acidic medium under standard conditions (298.15 K, 1 atm) in order to explore the properties of the fuel cell. The results showed that all structures are stable at the potential range 0–5.87 V. Formation energy, Mulliken charge and HOMO-LUMO energy calculations showed that Cu2–N6/Gr and Cu2–N8/Gr are more stable structure-wise, while free energy calculations showed that only Cu2–N8/Gr and Cu–N4/Gr structures support spontaneous ORR. The maximum cell potential under standard conditions was shown at 0.28 V and 0.49 V for Cu2–N8/Gr and Cu–N4/Gr respectively. From the calculations, the Cu2–N6/Gr and Cu2–N8/Gr structures are less favorable in H2O2generation; however, Cu–N4/Gr showed the potential for H2O2generation. In conclusion, Cu2–N8/Gr and Cu–N4/Gr are more favorable to ORR than Cu2–N6/Gr.