A sealing apparatus that includes a first mold in which a core is formed and a second mold in which a skin is formed which are combined to attach the core and the skin to seal a foaming space between the core and the skin. The apparatus further includes a slide mold installed to be moved horizontally in the first mold or the second mold to be moved forward by a restoring force of a support member to attach the skin to the core. The resilient support member is installed to support the slide mold and a position constraining member is coupled to the slide mold to release the constraint of the slide mold to allow the slide mold to be moved forward when the foaming space is sealed while the movement of the slide mold is constrained.