Copper powder, carbon fibers arranged in random directions and a metal capable of reacting with carbon fibers are homogeneously mixed together, and the mixture is heated and molded under high pressure to form an integral composite. The so formed carbon fiber-copper matrix composite has no directional characteristic in mechanical properties, and the linear thermal expansion coefficient of the composite is low and the thermal stability of the composite is so high that when it is exposed to high temperature, no damage by thermal deformation is caused.