A pitch is disclosed which is used as a raw material for making carbon fibers. The pitch has a quinoline insoluble content of 7-18% by weight and a toluene insoluble content of 70-90% by weight. Further, the pitch preferably has a n-heptane soluble content of 1.0% by weight or less. A process for producing the pitch is also disclosed. The process comprises carrying out thermal modification of a petroleum heavy residual oil having a boiling point of 400° C. or more (atmospheric pressure) and a sulfur content of 1.5% by weight or less. Insoluble substances are then separated and removed by heating at a temperature of 380° C. or less. Thereafter, a low boiling point fraction is removed by vacuum distillation. The pitch can be utilized to producd carbon fibers without breaking of filaments in spinning or adhesion by fusion of the fibers in infusibilization. The carbon fibers produced have a high tensile strength and high modulus of elasticity.