Since dual-metal single-atom catalyst (CoZnN/C) has been experimentally synthesized by atomically arching CoZn on Ndoped carbon nanofibers and exhibited potential electrocatalysis activity towards oxygen reduction reaction (ORR), we perform first-principles calculations to identify the highly active sites at different defects by comparing the four-step ORR processes on the constructed four CoZnN 6 models on graphene. The corresponding N-edge effect, dopant effect, and C-edge ring-closing effect are evaluated with the ORR evolution on different bonding environments, including pristine CoZnN 6 (OH), nanoribbon (NR) along zigzag direction, substitution of carbon/ oxygen (C/O substitution), and C-edge ring-closing configurations. OH-ligand is shown to significantly improve the ORR activities for all the considered structures. Especially, Csubstituted CoZnN 6 (OH), NR-CoZnN 5 O(OH) and CoZnN 6 (OH) with C-edge-effect exhibit obviously reduced overpotentials (η lim = 0.28, 0.48 and 0.41 V) of rate-determining steps among all the considered nine candidates. By plotting the relationship between the limiting potentials (U lim ) and free energies of intermediate *OH (ΔG OH* ), two prior catalysts of pristine-CoZnN 5 C(OH) and defect-CoZnN 6 CH(OH) are located near the top of the volcano curve with higher U lim = 0.95 and 0.82 V than Pt(111) (U lim = 0.80 V), implying that C-substitution could facilitate ORR performance in pristine-and defect-CoZnN 6 (OH) bonding situation.