Abstract: A catalyst for an oxygen reduction reaction containing catalyst particles having a shell-core structure containing a PtCo alloy or a PtCoMn alloy as a core, and platinum as a shell layer. A specific plane of a face-centered cubic lattice is formed by a plurality of platinum atoms contained in the shell layer, and a lattice constant of the plane of the face-centered cubic lattice on the catalyst particle surface is 3.70 ? or more and 4.05 ? or less (in a PtCo alloy), or 3.870 ? or more and 4.10 ? or less (in a PtCoMn alloy). A catalyst design method includes a step of calculating, with respect to an orientation plane such as the plane formed by platinum atoms of the shell layer, adsorption energies for an oxygen molecule, an OH group and a water molecule by first-principles calculation based on density functional theory.