The carbon electrode material of the present invention is used for a vanadium redox-flow cell. The carbon electrode material has quasi-graphite crystal structure in which <002> spacing obtained by X-ray wide angle analysis is 3.43 to 3.60 .ANG., size of a crystallite in c axial direction is 15 to 33 .ANG. and size of crystallite in a axial direction is 30 to 70 .ANG.. In addition, an amount of surface acidic functional groups obtained by XPS surface analysis is 0.1 to 1.2% and total number of surface bound-nitrogen atoms is 5% or smaller relative to total number of surface carbon atoms. The carbon electrode materials formed of a non-woven fabric of a carbonaceouss fiber is preferable.