PURPOSE: To provide a gas turbine combustor which achieves a higher cooling performance of a tail cylinder of a combustor to allow maintaining of sufficient endurance and reliability even in application for a high temperature gas turbine.

CONSTITUTION: In a combustor for a gas turbine in which an air passage for combustion is formed between a liner outer cylinder and a liner inner cylinder, a combustion chamber is defined in the liner inner cylinder and a tail cylinder 20 is provided in the liner inner cylinder to guide a combustion gas, the tail cylinder 20 is built in a double cylinder structure comprising an outer cylinder 22 of the tail cylinder and an inner cylinder 21 of the tail cylinder and a circular part thereof is formed into a cooling passage 23 leading to the air passage for combustion and a plurality of cooling fins 24 are arranged radially in the cooling passage 23.