with a catalyst comprising super fine metal particles for example iron nickel iron nickel alloy etc with a grain size of 100 to 300 u00e5 in a reaction zone at 900 u00b0 1500 u00b0 c and decomposing them the thus obtained carbon fibers are applied with a heat treatment at a temperature of from 1500 u00b0 to 3500 u00b0 c preferably 2500 u00b0 to 3000 u00b0 c for 3 to 120 min preferably 30 to 60 min in an inert gas atmosphere such as argon and formed into graphite fibers having a three dimensional crystal structure in which the carbon hexagonal network faces are substantially in parallel with the axis of fibers and oriented in a coaxial manner in this case if the heat treatment temperature is lower than 1500 u00b0 c the crystal structure of carbon does not develop sufficiently on the other hand if the temperature exceeds 3500 u00b0 c the effect is not enhanced particularly and it is not economical further if the heating treating time is shorter than 10 min the effect of the heat treatment is not sufficient to cause great deviation in the degree of the development of the crystal structure on the other hand if it exceeds 120 min no further improvement can be recognized the thus obtained carbon fibers may be applied with a purification treatment if necessary before or after the heat treatment.