The disclosure relates to a method for operating a gas turbine plant which is supplied with a fuel gas via a compressor station. The compressor station includes a compressor which compresses the fuel gas which is fed via a gas feed line and delivers it via at least one control valve to a combustion chamber of the gas turbine plant. A bypass system is arranged in parallel to the compressor via which fuel gas can be directed in a switchable manner past the compressor to the at least one control valve. An energy-saving operation can be achieved in a simple manner by continuously measuring the fuel gas pressure at the outlet of the at least one control valve. A minimum fuel gas pressure, which is desired (e.g., necessary) for operation of the gas turbine, at the inlet of the at least one control valve is determined from the measured pressure values in each case. The compressor station can be switched over to bypass operation when the fuel gas pressure which reaches the inlet of the at least one control valve via the bypass system is greater than or equal to the minimum fuel gas pressure.