NOVELTY - A catalyst for a fuel cell, comprising a carrier; and an active metal dispersion supported in the carrier, where the active metal has dispersity (Dp) of 0.01-1, is new.    USE - As a catalyst for a fuel cell, membrane-electrode assembly, and fuel cell system (claimed).    ADVANTAGE - The catalyst provides excellent efficiency and improves performance of fuel cell system over known fuel cell system.    DETAILED DESCRIPTION - A catalyst for a fuel cell, comprising a carrier; and an active metal dispersion supported in the carrier, where the active metal has a dispersity (Dp) of (X-X10/(X1-B))x (B'/X)2 i.e. 0.01-1, where X indicates the specific surface area (m2/g) of an active metal calculated using the average particle diameter of the active metal acquired from X-ray diffraction spectrum using a CuK alpha ray and its density, where X10 indicates the specific surface area (m2/g) of an active metal calculated using the particle diameter and density of the active metal when it had a particle diameter of 10 nm, where X indicates the specific surface area (m2/g) of an active metal calculated using the particle diameter and density of the active metal when it had a particle diameter of 1 nm, and where B' indicates the specific surface area (m2/g) of an active metal calculated from the specific surface area of a catalyst for a fuel cell acquired through a BET (Brunauer, Emmett, Teller) analysis is new. INDEPENDENT CLAIMS are included for the following:    (1) membrane-electrode assembly for a fuel cell, comprising a cathode and an anode facing each other; and a polymer electrolyte layer disposed between the cathode and the anode, where the cathode comprises a cathode substrate and a cathode catalyst layer, where the anode comprises an anode substrate and an anode catalyst layer, and where either the cathode catalyst layer or the anode catalyst layer comprises the catalyst; and    (2) a fuel cell system comprising an oxidizing agent supplier; a fuel supplier; and an electrical generator, where the electrical generator comprises a membrane-electrode assembly and a separator, where the membrane-electrode assembly comprises a cathode and an anode facing each other and a polymer electrolyte layer disposed between the cathode and the anode, where the cathode comprises a cathode substrate and a cathode catalyst layer, the anode comprises a platinum-based metal comprises an anode substrate and an anode catalyst layer, where either the cathode catalyst layer or the anode catalyst layer comprises the catalyst.