Fe(Co)-Nx/C is an important candidate catalyst for the next generation proton exchange membrane fuel cells (PEMFC), but the relationship between the structure and the oxygen reduction activity is still unclear. In this work, the different active site structures of Fe(Co)-Nx/C are explored and the oxygen reduction catalytic mechanisms are studied by means of density functional theory (DFT). Different kinds of Me-Nx/C motifs, including the edge site around the graphene sheet and the internal site in the graphene sheet (as well as in the graphyne sheet), are constructed and investigated. The calculated results suggest that for the edge active sites, high O2 adsorption strength may result in direct oxidation of metal ions thus losing their catalytic activity. The internal active sites are stable in acidic solution and display catalytic ability of oxygen reduction. The catalytic activity of the internal site is affected by three factors: the kind of internal metal ion, the bonded nitrogen or carbon atoms with metal ions and the size of the graphene sheet.