Metal-N-doped carbon is a promising replacement for non-precious-metal catalysts such as Pt for the oxygen reduction reaction (ORR) in polymer electrolyte membrane fuel cells (PEMFCs). Although these materials have relatively good catalytic activity and are cost-effective, they still have lower ORR activity than Pt, and so improving their performances is greatly required. In this study, high-throughput screening was employed based on density functional theory (DFT) calculations to search for good candidate catalysts with a transition metal atom coordinated by heteroatoms (B, N, S, O, and P) embedded in a graphene structure. In addition, coordinating a transition metal with two types of heteroatom dopants in a graphene structure was also considered. We calculated the binding energies of ORR intermediates on metal-heteroatom-based graphene structures because they are known to play a key role in ORR. Based on our results, the new group of electrocatalysts imparts excellent ORR activity for PEMFCs, and we suggest that our approach provides useful insight into exploring other promising candidate catalysts.