An encapsulation apparatus capable of securely sealing a gap of a display panel and improving intensity of the display panel, and a method of manufacturing an organic light emitting display device using the encapsulation apparatus are taught. The encapsulation apparatus includes an injection port having tapered projecting edges formed in both sides of one end the injection port, and injecting a reinforcing material into a gap of a display panel in a dual surface contact manner, the first substrate and the second substrate being attached to each other using a sealant; and a supporter coupled to the injection port and supporting the injection port.