TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Component: The electrodes for a fuel cell have a membrane containing ion conductive material and a collector with the membrane formed. The layer comprising the carbon nano-fiber carrying the fuel cell catalyst formed on the surface of the porous layer is impregnated with the ion conductive material. The fuel cell comprises a cathode electrode, an anode electrode and an electrolyte membrane arranged between the cathode electrode and the anode electrode. The fuel cell electrode has a porous catalyst carry medium containing conductive fibers having two particle size distribution peaks; a first particle diameter distribution peak existing at the small particle size side and a second particle size distribution peak; the catalyst carried on the conductive fibers belonging to the first particle size distribution peak; and a proton conductive material adhered on the conductive fiber surfaces so as to contact the catalyst. The lumps of the conductive fibers belonging to the first particle size distribution peak are scattered in the skeleton in which the conductive fibers belonging to the second particle size distribution peak are scattered.Preferred Parameter: The C-faces of the graphite crystal in the electrodes for fuel cell comprising the carbon nano-fibers are angled at 45-90degrees in the longitudinal direction. A mean number density of the catalysts for the fuel cell carried on the carbon nano-fibers is more than l x 1016/m2. The particle size value of the first particle size distribution peak is more than 5 times of the particle size value of the second particle size distribution peak in the third fuel cell electrode. The porous medium has two layers in different precision.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Parameter: A mean particle size of the irreducible inorganic material particles is smaller than a mean particle size of the metal particles. The carbon fibers in mean diameters of 100-1000 nm have specific surface area according to the BET method of 200-500 m2/g.Preferred Material: The irreducible inorganic material particles are alumina particles. The second element includes nickel, iron, cobalt, or copper. The catalyst material for the fuel cell includes carbon nano-fibers and catalyst particles carried on the carbon nanofibers, in which the abundance ratio of the carbon nano-fibers is more than 10%.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Parameter: A mean particle size of the irreducible inorganic material particles is smaller than a mean particle size of the metal particles. The carbon fibers in mean diameters of 100-1000 nm have specific surface area according to the BET method of 200-500 m2/g.Preferred Material: The irreducible inorganic material particles are alumina particles. The second element includes nickel, iron, cobalt, or copper. The catalyst material for the fuel cell includes carbon nano-fibers and catalyst particles carried on the carbon nanofibers, in which the abundance ratio of the carbon nano-fibers is more than 10%.