A press molding die structure having a paired press lower die and press upper die that are relatively movable to each other in which a work transferred into a portion between the press lower die and the press upper die is press-molded thereby to form a molded work. A concave portion is formed to a molding surface of the press lower die, and a suction cup of a vacuum stabilizer is provided to the concave portion formed to the molding surface of the press lower die, wherein the suction cup elastically sucks and retains the work at least at a time when the press molding dies are opened, thereby stabilizing a posture of the work.