Single-atom catalysts present extraordinary catalytic performance towards various reactions. In this work, the possibility of single Co atoms supported by the experimentally available defective two-dimensional boron nitride material (2D-BN) with boron vacancies (Co/BN) as a potential catalyst for the oxygen reduction reaction (ORR) was investigated by density functional theory. Co/BN has a similar active center to the cobalt nitride species, which have been proved to be effective ORR catalysts. It is found that Co atoms bind with the defective 2D-BN strongly to ensure the stability of Co/BN. Moreover, all of the ORR intermediates can be adsorbed on Co/BN. Especially, the HOOH species is found to be unstable and decomposes into two OH species immediately, suggesting that the ORR process occurs on Co/BN only through a direct 4e- pathway. Along the favorable pathway, the reduction of O2 to OOH is the rate-limiting step with a largest activation barrier of 0.30 eV and the maximum free energy change is 0.82 eV. Co/BN exhibits competitive ORR activity with that of CoN3 embedded graphene and Pt-based catalysts. These results should be enlightening to understand the ORR mechanism on Co/BN and design novel single-atom catalysts for the ORR and other electrocatalysis reactions.