A method of preparing a fuel cell electrode catalyst by preparing a platinum-carbon core-shell composite, which has a platinum nanoparticle core and a graphene carbon shell, using a simultaneous evaporation process, a method for preparing a fuel cell electrode comprising the catalyst prepared thereby, and a fuel cell comprising the same. A fuel cell comprising an electrode catalyst consisting of the core-shell composite prepared by simultaneously evaporating the platinum precursor and the organic precursor can have high performance and high durability, because the platinum particles are not agglomerated or detached and corroded even under severe conditions, including high-temperature, long use term, acidic and alkaline conditions.