Abstract: A gas turbine combustor 1 prevents an inequality of distribution of temperatures at the outlet of the combustor which might otherwise be caused by cooling air introduced into the combustor. A liner 2 having an outer liner 2' and an inner liner 2", is disposed within a casing 3 of the gas turbine combustor 1. The liner 2 is composed of a liner inner cylinder 15, having liner cooling paths 16, and a liner outer cylinder 14. Fuel supplied via upstream side manifolds 9 and 10 flows through the liner cooling paths 16 and is discharged from a downstream side manifold 11 after cooling the liner 2. The fuel is boosted by a pump and is supplied to a fuel-air pre-mixer 13 from a fuel supply port 12 so as to be burned in the combustion chamber.