Dual-metal-site catalysts (DMSCs) are emerging as a new frontier in the field of oxygen reduction reaction (ORR). However, there is a lack of design principles to provide a universal description of the relationship between intrinsic properties of DMSCs and the catalytic activity. Here, we identify the origin of ORR activity and unveil design principles for graphene-based DMSCs by means of density functional theory computations and machine learning (ML). Our results indicate that several experimentally unexplored DMSCs can show outstanding ORR activity surpassing that of platinum. Remarkably, our ML study reveals that the ORR activity of DMSCs is intrinsically governed by some fundamental factors, such as electron affinity, electronegativity, and radii of the embedded metal atoms. More importantly, we propose predictor equations with acceptable accuracy to quantitatively describe the ORR activity of DMSCs. Our work will accelerate the search for highly active DMSCs for ORR and other electrochemical reactions.