A function ally gradient composite material containing copper and carbon as main components and having a predetermined shape, in which the composition ratio of the copper to the carbon in the material continuously varies in at least one predetermined direction. The material is manufactured, for example, by impregnating carbon felt with a resin and thermo-compressively molding the impregnated felt (step S101), carbonizing the resin by baking (step S102) to provide a preformed carbon material (step S104). Pyrolytic carbon is thereafter deposited in the preformed carbon material by the CVI method (step S105) to provide a carbon material having the bulk density varying in a predetermined direction (step S107). After the wettability of the carbon material against copper is improved by siliconization (step S108), pores of the carbon material are impregnated with copper (step S109) to obtain a functionally gradient composite material of copper and carbon.