Based on DFT calculations, we investigated the activity and the stability of three octahedral Ag nanoparticles (Ag19, Ag85, and Ag146) for catalytic oxygen reduction reaction (ORR) and further compared their ORR performance with an outspread flat Ag(111) surface and a Pt(111) surface. The results indicate that Ag19 cannot be used as an effective ORR catalyst mainly due to its poor stability in the electrochemical environment. In contrast, both Ag85 and Ag146 possess higher surface cohesive energies and cluster cohesive energies, indicating that they have relatively lower thermodynamic tendency to electrochemical dissolution. In addition, both of these two nanoparticles also have high catalytic activities, as suggested by the calculated highest potentials of 0.80 and 0.76 V. Therefore, our current study indicates that an octahedral Ag nanoparticle with the diameter of ∼2 nm should have good catalytic activity and stability for ORR.