PURPOSE: A connection structure of a culvert and a connection method thereof are provided to facilitate the connection of culverts, prevent the lowering of water-tightness due to differential settlement, and save material costs. CONSTITUTION: A connection structure of a culvert comprises a buried member(40), a fixing member(50), a wedge cone member(60), a wedge(70), and a connecting bar(30). The buried member are buried under both sides of the culvert and formed with a hollow(41) and a flange(42). The fixing member is inserted into the front end of the buried member. The fixing member has a female thread(51), a through-hole, and a support(53). The wedge cone member is combined with the fixing member. The wedge cone member has a male thread(61), a flange(62), and a wedge hole(63). The wedge is inserted into the wedge hole and has a fastening hole(71). The connecting bar is inserted into the side of the culvert.