Dual-/multi-heteroatom-doped carbon nanomaterials have been demonstrated to be effective bi-/multi-functional catalysts for the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER), the critical reactions in fuel cells and metal–air batteries, respectively. However, trial-and-error routes are usually used to search for better catalysts from multi-doped complex material systems, and establishing design principles or intrinsic descriptors would accelerate the discovery of new efficient catalysts. Here, a descriptor based on p_z-orbitals of active sites is proposed to describe the catalytic performance of dual-/tri-element-doped graphene catalysts for the ORR and the OER. In addition to multiple doping, the established descriptor is universal in nature and can also predict the contributions of defects and edges or their combinations. The prediction capacity of the descriptor is further enhanced by introducing a correction factor based on crystal orbital Hamilton population (COHP) analysis, which reveals the differences between the adsorption mechanism of edged C and graphitic C on graphene. The predictions are consistent with DFT calculations and experimental results. This work provides a powerful tool for rapidly screening multi-doped complex material systems for the desired ORR and OER bifunctional catalysts.