Bio-inspired non-precious-metal catalysts based on iron and cobalt porphyrins are promising alternatives to replace costly platinum-based catalysts for oxygen reduction reaction (ORR) in fuel cells. However, the exact nature of the active sites is still not clearly understood, and further optimization design is needed for practical applications. Here, we report a rational catalyst design process by combining density functional theory (DFT) calculations and experimental validations. Two sets of square-planar (MNxC4-x) and square-pyramid (MNxC5-x) active centers (M=Mn, Fe, Co, Ni) incorporated in graphene were examined using DFT. Fe-N-5 and Co-N-4 sites were identified theoretically to have the best performance in fuel cells, while Ni-NxC4-x sites catalyze the most H2O2 byproduct. Graphene samples with well-dispersed incorporations of metals were synthesized, and the following electrochemical measurements show an excellent agreement with the theoretical predictions, indicating that a successful design framework and systematic understanding toward the catalytic nature of these materials are established.