Over past years, the excessive use of fossil fuel has posed serious problems such as greenhouse effect and environmental pollution, which threaten human life. Regarded as an ideal substitution for traditional internal combustion engine, low temperature proton exchange membrane fuel cell (PEMFC) converts chemical energy through electrode reaction directly into electrical energy with high efficiency and low pollution. However, the main problem behind the industrialization of PEMFC, is that oxygen reduction reaction (ORR) occurring on the cathode needs precious metal platinum (Pt) as catalyst, which has a limited reserve and is costly. Owing to high activity and stability, the graphenes doped with non-metal B and P, have proven to be excellent alternatives to Pt experimentally. However, the relevant theoretical work is scarce. Adsorptions of the ORR intermediates, i.e., O, O-2, OH, and OOH, of doped graphenes are essential for the cathode reaction, which also bring some difficulties to the next step reaction. Therefore, in this paper, based on density functional theory, the adsorption characteristics of O, O-2, OH, and OOH of B-doped, P-doped and B, P-codoped graphenes are studied using first-principles calculation code VASP first. By analyzing the adsorption energies, bond lengths, densities of states and charge transfers, the influences of the different dopants on the intermediates are evaluated. Then, the ORR steps are discussed, and the free energy change of each step is further given. The results show that for B-doped and P-doped graphenes, the adsorption energies of various intermediates exhibit similar linear relationships. The adsorption energy of OOH of P-doped graphene (3.26 eV) is much larger than that in B-doped grapheme (0.73 eV). The large adsorption energy of P-doped graphene is beneficial to the fracture reaction of O-O bond in OOH, while the small adsorption energy of B-doped graphene can promote the reaction of OH converting into water. Owing to the synergistic effect, the graphene codoped with B and P possesses better catalyzing ability than single B-and P-doped ones. The results are helpful for understanding the excellent performances of codoped graphenes.