Method for producing a precursor pitch for carbon fiber

Precursor pitch to be used for formation of carbon fiber is produced by heating a coal tar soft or middle pitch at a temperature of 350 DEG -500 DEG C. at a first stage to form mesophase, extracting the thus treated pitch with a solvent, separating and removing the solvent insoluble portion including mesophase to obtain a pitch containing no free carbon and further at the second stage heat-treating the pitch containing no free carbon in an inert gas atmosphere under atmospheric pressure or a reduced pressure under the following condition 600-1.2 T