The activity of nanomaterials (NMs) in catalytically scavenging superoxide anions mimics that of superoxide dismutase (SOD). Although dozens of NMs have been demonstrated to possess such activity, the underlying principles are unclear, hindering the discovery of NMs as the novel SOD mimics. In this work, we use density functional theory calculations to study the thermodynamics and kinetics of the catalytic processes, and we develop two principles, namely, an energy level principle and an adsorption energy principle, for the activity. The first principle quantitatively describes the role of the intermediate frontier molecular orbital in transferring electrons for catalysis. The second one quantitatively describes the competition between the desired catalytic reaction and undesired side reactions. The ability of the principles to predict the SOD-like activities of metal-organic frameworks were verified by experiments. Both principles can be easily implemented in computer programs to computationally screen NMs with the intrinsic SOD-like activity.