The present invention relates to a connection structure of a metal corrugated pipe, which is used to connect metal corrugated pipes with each other or to connect a metal corrugated pipe to a boiler combustor. The connection structure includes a first connection member having one side, in which an external thread is formed on an outer surface of the one side and an inner surface of the one side has a diameter gradually reduced to form an inclined surface; a second connection member formed on an inner surface thereof with an internal thread screw-coupled with the external thread; and a heat-resistant packing fitted on the outer surface of the metal corrugated pipe, in which a front end of the heat-resistant packing is compressed by the inclined surface as the first connection member is screw-coupled with the second connection member.