Pt nanoparticles (NPs) in a proton exchange membrane fuel cell as a catalyst for an oxygen reduction reaction (ORR) fairly overbind oxygen and/or hydroxyl to their surfaces, causing a large overpotential and thus low catalytic activity. Realizing Pt-based core-shell NPs (CSNPs) is perhaps a workaround for the weak binding of oxygen and/or hydroxyl without a shortage of sufficient oxygen molecule dissociation on the surface. Towards the end, we theoretically examined the catalytic activity of NPs using density functional theory; each NP consists of one of 12 different 3d-5d transition metal cores (groups 8-11) and a Pt shell. The calculation results evidently suggest the enhancement of catalytic activity of CSNPs in particular when 3d transition metal cores are in use. The revealed trends in activity change upon the core metal were discussed with respect to the thermodynamic and electronic structural aspects of the NPs in comparison with the general d-band model. The disparity between the CSNP and the corresponding bilayer catalyst, which is the so-called size effect, was remarkable; therefore, it perhaps opens up the possibility of size-determined catalytic activity. Finally, the overpotential for all CSNPs was evaluated in an attempt to choose promising combinations of CSNP materials.