A turbo cluster gas turbine system includes: at least one combustor configured to combust a fuel to generate a combustion gas; an output turbine configured to be driven with the combustion gas from the at least one combustor; and a plurality of supercharging systems configured to supply compressed air to be supplied to the at least one combustor, wherein each of the supercharging systems includes: a first turbocharger having a rotation shaft formed separately from a rotation shaft of the output turbine and configured to be driven with the combustion gas from the combustor; a first air line for supplying compressed air compressed by a compressor of the first turbocharger to the combustor; and a first combustion gas line for supplying the combustion gas from the combustor to a turbine of the first turbocharger.