A gas turbine combustor is provided with a combustor basket where combustion gas flows, the combustion gas being produced by combustion of fuel injected from a nozzle, and a first resonance device and a second resonance device mounted on an outer surface of the combustor basket. The second resonance device is disposed on a downstream side from the first resonance device in a flow of the combustion gas and damps combustion oscillation of a frequency higher than the first resonance device. The first and second resonance devices are acoustic liners each having a housing mounted to the outer surface of the combustor basket. A resonance space surrounded by the housing and the outer surface of the combustor basket communicates with an interior space of the combustor basket via a plurality of acoustic holes formed in the combustor basket.