PURPOSE: To obtain a heat resistant high strength titanium aluminide base composite material excellent in compatibility of the reinforcing material with the matrix by using tungsten fibers as a reinforcing material and γ-TiAl as a matrix.

CONSTITUTION: Tungsten fibers as a reinforcing material are incorporated into γ-TiAl as a matrix preferably by 5-60% to obtain the objective titanium aluminide base composite material. The tungsten fibers are, e.g. fibers contg. ThO2, HfC, etc., in pure tungsten. The TiAl is an intermetallic compd. Since the tungsten fibers are excellent in compatibility with the γ-TiAl, the objective sound composite material is obtd. by combination.