A method for producing a catalyst supporting a metal or an alloy on a support, including: independently controlling a temperature of a first supercritical fluid to be first temperature, the first supercritical fluid containing a precursor of the metal or precursor of the alloy that is dissolved in a supercritical fluid; independently controlling a temperature of the support to be a second temperature higher than the temperature of the first supercritical fluid; and supplying the first supercritical fluid controlled to the first temperature to the support, to cause the metal or the alloy to be supported on the support.