A liquefied natural gas compression system includes: a first gas turbine that drives a rotary machine; a first steam boiler including a first heat recovery steam generator that recovers heat from exhaust gas from the first gas turbine; a first steam turbine that drives a first refrigerant compressor; a common header steam line through which steam from the first steam boiler flows to an inlet of the first steam turbine; an auxiliary steam line; and a letdown valve that connects the common header steam line to the auxiliary steam line and that opens in response to pressure of the common header steam line exceeding a predetermined threshold value.