NOVELTY - The method for producing a catalyst-layer-supporting substrate, comprises forming a laminate of metal catalyst layer (2) and mixture layer (3) on a substrate by repeating a first step and a second step at 5-100 times, and subjecting the laminate to an acid treatment. The first step is a step of sputtering or depositing the metal catalyst layer having a catalyst. The second step is a step of sputtering or depositing the mixture layer of carbon and metal. The metal catalyst layer has a thickness of 5-100 nm per one layer.    USE - The method is useful for producing a catalyst-layer-supporting substrate, which is useful in a membrane-electrode assembly and a fuel cell (claimed).    ADVANTAGE - The method effectively produces the catalyst-layer-supporting substrate, which prevents the aggregation of catalyst fine particles, thus controlling the pore structure of the catalyst layer and increasing the density of the three-phase interface in fuel/catalyst/proton conductive material.    DETAILED DESCRIPTION - The method for producing a catalyst-layer-supporting substrate, comprises forming a laminate of metal catalyst layer (2) and mixture layer (3) on a substrate by repeating a first step and a second step at 5-100 times, and subjecting the laminate to an acid treatment. The first step is a step of sputtering or depositing the metal catalyst layer having a catalyst. The second step is a step of sputtering or depositing the mixture layer of carbon and metal. The metal catalyst layer has a thickness of 5-100 nm per one layer. The mixture layer has a composition of C1xMx with the proviso that x satisfies a condition of 0.9-2, and has a thickness (10-150 nm) per one layer. INDEPENDENT CLAIMS are included for:    (1) a method for producing a membrane-electrode assembly; and    (2) a method for producing a fuel cell.    DESCRIPTION OF DRAWING(S) - The diagram shows an exemplary view of a catalyst synthesis process.    Substrate (1)    Metal catalyst layer (2)    Mixture layer. (3)