The positron-lifetime spectrum for cup-stacked carbon nanofibers (CNFs) is composed of three components: 0.125 ns (fixed) (6%), 0.345 ns (75%), 1.21 ns (19%). The longest-lived component assigned to ortho-positronium (o-Ps) verifies a prominent yield of o-Ps, which is in contrast with the fact that no o-Ps is detected for uncapped cylindrical multi-walled carbon nanotubes. CNFs heat-treated to 1073 K in vacuo showed a positron-lifetime spectrum the same as that of untreated CNFs, which demonstrates that the thermal detachment of some functional groups from the surface of the CNFs does not change the Ps yield. The yield is found almost independent of temperature between 10 and 280 K. A single CNF, ca. 50 nm in outer diameter, observed by transmission electron-microscopy, comprises stacked cups of 9similar to12 truncated conical graphene sheets at ca. 20degrees with respect to the fiber axis, so that all edges of graphene sheets are found on the zigzag outer- as well as inner-surfaces of the fiber. The Raman spectrum for CNFs exhibits a band of a disorder-induced mode at 1349 cm(-1) (D-band) and a band of the E(2g2) in-plane mode at 1577 cm(-1) (G-band). The intensity-ratios of a D-band to a G-band are 0.17, 0.25 and 0 for a mat of CNFs, the edge plane and the basal plane of a highly oriented pyrolitic graphite block, respectively. For graphite materials, Ps is formed from the positrons trapped in the defects originating from edges of graphene sheets.