Abstract: A graphite fiber having an elastic modulus E of 340-680 GPa, a microvoid radius of not larger than 20 .ANG. and a crystal size L.sub.c (.ANG.) satisfying the following formula:L.sub.c.sup.3 .ltoreq.0.918.times.10.sup.3 E-3.times.10.sup.5is valuable for a composite material having an improved compression strength. The graphite fiber is made preferably by oxidizing an acrylonitrile polymer precursor containing 0.05-8 wt. % of comonomer units and having an iodine adsorption amount of not larger than 3 wt. % and an orientation degree of at least 85%, at 200.degree.-300.degree. C. in an oxidative atmosphere under tension to obtain an oxidized fiber having a water adsorption of not larger than 7 wt. % and an orientation degree of at least 78%, followed by carbonization and graphitization of the oxidized fiber under tension.