TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: The metal catalyst is directly provided on surface (10a) of the base material. The carbon nanofiber structure is obtained by supplying gas containing oxygen molecule to carbon nanofiber-forming structure from surface opposite to the metal catalyst, and growing carbon nanofiber. In the nanofiber aggregation layer, the carbon nanofibers are gathered, such that hole having hole diameter of 0.3-7 mu m is formed. During manufacture of carbon nanofiber structure, the carbon nanofiber-forming structure is heated at 500 degrees C. The hole in the carbon nanofiber-forming structure forms an opening part in the surface (10a) of the base material, and the metal catalyst is formed on the area (excluding the opening portion among the surface (10a)) of the base material. Preferred Composition: The carbon nanofiber-forming structure further has metal oxide layer containing metal oxides between surface (10a) of the base material and the metal catalyst. The metal oxide is aluminum oxide. A metal oxide layer portion has mutually spaced thin portions having thickness of 0.5-10 nm, and thick portion having thickness of more than 10 nm. The metal catalyst includes vanadium, molybdenum, iron, cobalt, nickel, palladium, platinum, rhodium, ruthenium and tungsten. The carbon nanofiber structure has carbon nanofiber aggregation layer in which carbon nanofibers orientated along direction away from the surface (10a) are gathered. The hole is through-hole. The oxygen ion-conductive oxide is high-temperature oxygen ion-conductive oxide which conducts oxygen ion at high temperature of 500 degrees C or more. Preferred Properties: At least one portion of the metal oxide layer has thickness of 0.5-10 nm, preferably 1-8 nm. The total area of the hole is 1-40% among the carbon nanofiber aggregation layer with respect to apparent area of end surface on side opposite to the base material. The length of the carbon nanofiber is more than maximum value of hole diameter of the hole.