A fiber reinforced composite member molding apparatus for molding a fiber reinforced composite member from stacked sheets of prepreg formed of long carbon fibers impregnated with resin, comprising: a pair of molds (2, 3) provided to be brought nearer to or away from each other, heat sources to heat the resin contained in the prepreg via the molds (2, 3) in a clamped and pressed state with the stacked sheets of prepreg clamped between the molds (2, 3), and cooling passages to allow a cooling fluid to flow, thereby cooling the resin via the molds (2, 3) after heating of the resin contained in the prepreg, wherein the molds (2, 3) each have a design surface (61, 72) brought into contact with the stacked sheets of prepreg, the design surface (61, 71) being divided into a plurality of regions, and a plurality of cells provided along the design surface (61, 71) to be open at the back of the design surface (61, 71) and individually correspond to the regions of the design surface (61, 71), the heat sources are individually arranged in the cells, the molds (2, 3) each comprise a base mold component (4, 5) and a design mold component (6, 7) providing the design surface (61, 71) and detachably attached to the base mold component (4, 5) with a thermal insulator interposed therebetween, and the base mold component (4, 5) and the design mold component (6, 7) of each of the molds (2, 3) have approximating opposing surfaces (46, 56, 66, 76) formed to approximate the design surface (61, 71), the molding apparatus being characterized in that the approximating opposing surfaces (46, 56, 66, 76) of the base mold component (4, 5) and the design mold component (6, 7) each comprising a plurality of polygonal planes (46a-46f, 56a-56f, 66a-66f, 76a-76f) arranged around a center of thermal expansion (460, 560, 660, 760) in heating of the resin contained in the prepreg and abutting each other, and wherein the base mold component (4, 5) and the design mold component (6, 7) are connected together by a connecting member running through the centers of thermal expansion (460, 560, 660, 760). a pair of molds (2, 3) provided to be brought nearer to or away from each other, heat sources to heat the resin contained in the prepreg via the molds (2, 3) in a clamped and pressed state with the stacked sheets of prepreg clamped between the molds (2, 3), and cooling passages to allow a cooling fluid to flow, thereby cooling the resin via the molds (2, 3) after heating of the resin contained in the prepreg, wherein the molds (2, 3) each have a design surface (61, 72) brought into contact with the stacked sheets of prepreg, the design surface (61, 71) being divided into a plurality of regions, and a plurality of cells provided along the design surface (61, 71) to be open at the back of the design surface (61, 71) and individually correspond to the regions of the design surface (61, 71), the heat sources are individually arranged in the cells, the molds (2, 3) each comprise a base mold component (4, 5) and a design mold component (6, 7) providing the design surface (61, 71) and detachably attached to the base mold component (4, 5) with a thermal insulator interposed therebetween, and the base mold component (4, 5) and the design mold component (6, 7) of each of the molds (2, 3) have approximating opposing surfaces (46, 56, 66, 76) formed to approximate the design surface (61, 71), the molding apparatus being characterized in that the approximating opposing surfaces (46, 56, 66, 76) of the base mold component (4, 5) and the design mold component (6, 7) each comprising a plurality of polygonal planes (46a-46f, 56a-56f, 66a-66f, 76a-76f) arranged around a center of thermal expansion (460, 560, 660, 760) in heating of the resin contained in the prepreg and abutting each other, and wherein the base mold component (4, 5) and the design mold component (6, 7) are connected together by a connecting member running through the centers of thermal expansion (460, 560, 660, 760).