We studied the oxygen reduction reaction (ORR) activities for two monolayer (ML)-thick Pt on PtxNi100-x(111) (Pt2ML/PtxNi100-x(111)) model core-shell catalysts fabricated by molecular beam epitaxy (MBE). Low-energy electron diffraction patterns for all Pt2ML/PtxNi100-x(111) showed six-fold surface symmetry with longrange ordering, indicating a (111) atomic arrangement of the topmost Pt shell layers. Furthermore, scanning tunneling microscopy images of the Pt2ML/Pt50Ni50(111) and Pt2ML/Pt25Ni75(111) surfaces exhibited Moiré-like height modulations, which are likely induced by large lattice mismatches between the topmost Pt(111) shell layers and the Pt-Ni(111) substrates. The ORR activity of Pt2ML/PtxNi100-x(111) increased with the Ni composition; the enhancement factors are 8-, 18-, and 25-fold vs. Pt(111) for Pt2ML/Pt75Ni25(111), Pt2ML/Pt50Ni50(111), and Pt2ML/Pt25Ni75(111), respectively. The results suggested that the Pt surface strains induced by lattice mismatches between the Pt shells and Pt-Ni substrates increased with the Ni composition, leading to a marked enhancement in ORR activity, particularly for Pt2ML/Pt25Ni75(111).