Intensive research on oxygen reduction reaction (ORR) catalysts has been undertaken to find a Pt substitute or reduce the amount of Pt. Ag nanoparticles are potential Pt substitutes; however, the weak oxygen adsorption energy of Ag prompted investigation of other catalysts. Herein, we prepared AgCu bimetallic nanoparticle (NP) systems to improve the catalytic performance and compared the catalytic performance of Ag, Cu, AgCu (core–shell), and AgCu (alloy) NP systems as new catalyst by investigating the adsorption energy of oxygen and the activation energy of oxygen dissociation, which is known to be the rate-determining step of ORR. By analyzing HOMO-level isosurfaces of metal NPs and oxygen, we found that the adsorption sites and the oxygen adsorption energies varied with different configurations of NPs. We then plotted the oxygen adsorption energies against the energy barrier of oxygen dissociation to determine the catalytic performance. AgCu (alloy) and Cu NPs exhibited strong adsorption energies and low activation-energy barriers. However, the overly strong oxygen adsorption energy of Cu NPs hindered the ORR.