In a combustor tail pipe (1) of a gas turbine using steam as a cooling medium, the temperature distribution in the axial direction of the tail pipe is put under a gently varying condition so as to prevent the occurrence of a large thermal stress, whereby the safety of the combustor tail pipe and the reliability of an apparatus are improved greatly. A general arrangement is made by providing a supply jacket (16) between upstream side and downstream side jackets (14, 15), and using the latter jackets (14, 15) as exhaust jackets. The upstream side exhaust jacket (14) is provided in a position downstream of a tail pipe inlet (2) and adjacent to a bypass passage (10), whereby a non-cooling section A is formed in the vicinity of the tail pipe inlet. On the downstream side, the supply jacket (16) is provided closer to the downstream side exhaust jacket in a reduced-diameter portion of the tail pipe so that the length of a cooling passage portion between the supply jacket and the downstream side exhaust jacket (15) is reduced.