The method allows to produce catalysts with nanoparticles of platinum and its alloys with metals of a given composition, with high values of catalytic activity in an oxygen electroreduction reaction, and with predetermined values of structural characteristics. The method comprises preparation of a solution of chloroplatinic acid or a mixture of chloroplatinic acid with metal salts, mixing thereof with dispersed carbon or non-carbon carriers, their mixtures and compositions with specific surface area of more than 60 m2/g, dispersion of the obtained mixture, chemical reduction of compounds of platinum and a metal salt with subsequent deposition of nanoparticles of metallic platinum or its alloys on a dispersed carrier being carried out by purging gases selected from: nitrogen oxides (N2O, NO, NO2), carbon oxides (CO, CO2), sulfur oxide (SO2), ammonia (NH3) or their mixtures through the solution at a temperature of the solution in the range from 5 to 98° C.