The invention discloses a flexible stretch-forming device and a method for carrying out stretch-forming on a plate by utilizing the flexible stretch-forming device and solves the technical problem that the stretch-forming accuracy of a flexible stretch-forming device for the molded surface of a reconfigurable unidirectional continuous die is low. The technical scheme includes that the flexible stretch-forming device comprises an industrial manipulator, a heating forming head, a power supply, a multipoint die, a nail post and a polyurethane elastic cushion. The nail post is mounted on the base of the multipoint die, the polyurethane elastic cushion is positioned above the nail post, the lower surface of the polyurethane elastic cushion is attached to the discrete surface formed by the nail head of the nail post, the plate is positioned above the polyurethane elastic cushion, the lower surface of the plate is attached to the upper surface of the polyurethane elastic cushion, the heating forming head is positioned above the plate, and the spherical head surface of the heating forming head is contacted with the upper surface of the plate. According to the flexible stretch-forming device and the method for carrying out stretch-forming on the plate by utilizing the flexible stretch-forming device, the electromagnetic induction heating forming head is adopted to locally heat the plate in the stretch-forming process, the local heat effect of the region can reduce the deformation resistance of the plate, the plasticity is improved, the resilience value is reduced, and the forming accuracy of the plate is improved.