Controlling nanoparticle (NP) surface strain, i.e. compression (or stretch) of surface atoms, is an important approach to tune NP surface chemistry and to optimize NP catalysis for chemical reactions. Here we show that surface Pt strain in the core/shell FePt/Pt NPs with Pt in three atomic layers can be rationally tuned via core structural transition from cubic solid solution [denoted as face centered cubic (fcc)] structure to tetragonal intermetallic [denoted as face centered tetragonal (fct)] structure. The high activity observed from the fct-FePt/Pt NPs for oxygen reduction reaction (ORR) is due to the release of the overcompressed Pt strain by the fct-FePt as suggested by quantum mechanics-molecular mechanics (QM-MM) simulations. The Pt strain effect on ORR can be further optimized when Fe in FePt is partially replaced by Cu. As a result, the fct-FeCuPt/Pt NPs become the most efficient catalyst for ORR and are nearly 10 times more active in specific activity than the commercial Pt catalyst. This structure-induced surface strain control opens up a new path to tune and optimize NP catalysis for ORR and many other chemical reactions.