A fuel-injection device in a turbomachine is disclosed. The device includes a high-pressure pump supplying a flow control valve, whose outlet is connected via a pressurization and cut-off valve to a fuel-injector feed pipe. The valve is connected to the inlet and to the outlet of the pump in order to define two fuel pressurization thresholds, one of which is used to start-up and restart the turbomachine and the other is used for operating the turbomachine from an idle speed and for commanding an equipment with variable geometry.