A fuel supply system for a turbomachine, comprising a fuel circuit comprising pressurizer at the output of the circuit, a pump arranged to send into the circuit a fuel flow rate which is an increasing function of the rotational speed of a shaft of the pump, and a control circuit arranged to control the device to comply with a flow rate setpoint at the output of the fuel circuit. The system further comprises a feedforward corrector circuit configured to calculate an increment of the flow rate setpoint as a function of the engine speed of the turbomachine and of a variation in the engine speed of the turbomachine, and to add this increment to the flow rate setpoint. A method of regulating the pump is also described.