A core molding apparatus and a core molding method capable of reducing the possibility of the deterioration in the calculation accuracy of the amount of supply of a raw material for a core are provided. A core molding apparatus includes: a kneading tank configured to knead a raw material for a core; a raw material supply unit configured to supply the raw material to the kneading tank; a mold configured to contain a kneaded material made of the raw material kneaded in the kneading tank and to mold the core; a piston configured to inject the kneaded material contained in the kneading tank into the mold; and a control unit configured to control an amount of supply of the raw material from the raw material supply unit to the kneading tank.