PtM-based core-shell nanoparticles are a new class of active and stable nanocatalysts for promoting oxygen reduction reaction (ORR); however, the understanding of their high electrocatalytic performance for ORR at the atomistic level is still a great challenge. Herein, we report the synthesis of highly ordered and homogeneous truncated cuboctahedral Pt3Co-Pt core-shell nanoparticles (cs-Pt3Co). By combining atomic resolution electron microscopy, X-ray photoelectron spectroscopy, extensive first-principles calculations, and many other characterization techniques, we conclude that the cs-Pt3Co nanoparticles are composed of a complete or nearly complete Pt monolayer skin, followed by a secondary shell containing 5-6 layers with similar to 78 at% of Pt, in a Pt3Co configuration, and finally a Co-rich core with 64 at% of Pt. Only this particular structure is consistent with the very high electrocatalytic activity of cs-Pt3Co nanoparticles for ORR, which is about 6 times higher than commercial 30%-Pt/Vulcan and 5 times more active than non-faceted (spherical) alloy Pt3Co nanoparticles. Our study gives an important insight into the atomistic design and understanding of advanced bimetallic nanoparticles for ORR catalysis and other important industrial catalytic applications.