The mesophase pitch based and melt blown discontinuous carbon fibers of a peculiar structure are provided. These fibers are characterized in that a large number of small domains, each domain has an average equivalent diameter of from 0.03 .mu.m to 1 .mu.m and has a nearly unidirectional orientation of folded carbon layers, assemble to form a mosaic structure on the cross-section of the said carbon fibers and that the folded carbon layers of each domain are oriented at an angle to the direction of the folded carbon layers of the neighboring domains on the boundary.