A carbon electrode material powder having an average particle diameter of not more than 10 μm and a single particle ratio of at least 0.7, wherein:- the coefficient of variation of the particle size distribution expressed in the following formula is not more than 0.65: coefficient of variation of particle size distribution = d 84 % − d 16 % / 2 × average particle diameter 1, where d 84 % and d 16 % represent particle sizes exhibiting cumulative where d 84% and d 16% represent particle sizes exhibiting cumulative frequencies of 84% and 16% in a frequency distribution obtained by laser diffraction scattering respectively; the sphericity is at least 0.7; the average particle diameter denotes a value of a cumulative frequency of 50% in a frequency distribution obtained by a measuring method employing a laser diffraction particle size measuring apparatus; the single particle ratio denotes the number of single particles / the total number of primary particles, the ratio determined by dispersing the carbon electrode material powder in water droplets, making an optical microscope observation and counting the total number of primary particles and the number of single particles in a randomly selected visual field containing 300 primary particles, the single particles being primary particles not forming secondary aggregates resulting from aggregation; and the sphericity denotes, in a case of randomly deciding a visual field containing 300 primary particles in an optical microscope observation, selecting 10 primary particles having the lowest aspect ratios, i.e. the ratios of minor axes / major axes, and measuring the aspect ratios in projected profiles thereof as to the respective ones of these 10 primary particles, the average of these 10 aspect ratios. the coefficient of variation of the particle size distribution expressed in the following formula is not more than 0.65: coefficient of variation of particle size distribution = d 84 % − d 16 % / 2 × average particle diameter 1, where d 84 % and d 16 % represent particle sizes exhibiting cumulative where d 84% and d 16% represent particle sizes exhibiting cumulative frequencies of 84% and 16% in a frequency distribution obtained by laser diffraction scattering respectively; the sphericity is at least 0.7; the average particle diameter denotes a value of a cumulative frequency of 50% in a frequency distribution obtained by a measuring method employing a laser diffraction particle size measuring apparatus; the single particle ratio denotes the number of single particles / the total number of primary particles, the ratio determined by dispersing the carbon electrode material powder in water droplets, making an optical microscope observation and counting the total number of primary particles and the number of single particles in a randomly selected visual field containing 300 primary particles, the single particles being primary particles not forming secondary aggregates resulting from aggregation; and the sphericity denotes, in a case of randomly deciding a visual field containing 300 primary particles in an optical microscope observation, selecting 10 primary particles having the lowest aspect ratios, i.e. the ratios of minor axes / major axes, and measuring the aspect ratios in projected profiles thereof as to the respective ones of these 10 primary particles, the average of these 10 aspect ratios.