A gas turbine combustor is provided in which product reliability and heat transfer promotion are compatible while suppressing an increase in pressure loss.In a gas turbine combustor comprising a combustor liner, an outer tube provided around an outer periphery of the combustor liner, and an annular flow passage in which a cooling medium (cooling air) flows and which is formed between an outer surface of the combustor liner and an inner surface of the outer tube, the outer tube includes an inner diameter reduced portion and a taper portion smoothly connecting the inner diameter reduced portion and an inner peripheral portion on an upstream side, and is provided at an inner surface of the taper portion with longitudinal vortex generating means generating a vortex that has a central rotation axis in a flowing direction of the cooling medium (cooling air).