Fuel metering circuit for turbomachine, comprising: - a fuel metering element, - a pump adapted to circulate a fuel flow towards the metering element, and - a control valve adapted to return, towards the pump, an excess fuel flow delivered to the metering element, as a function of a difference in fuel pressure at the terminals of the metering element, the control valve being adapted to modulate the excess flow returned towards the pump as a function of variations in fuel density delivered to the metering element, said fuel metering circuit further comprising a high-pressure line for feeding the metering element and a low-pressure line for returning to the pump, characterized in that it also comprises: - a flow extraction line connecting the high-pressure line to a chamber of the control valve, said line comprising a pump adapted to deliver to said chamber a constant fuel flow at a pressure higher than the pressure of the fuel in the high-pressure line, and - a flow return line connecting the chamber to a fuel recirculation inlet of the high-pressure line, said line comprising a diaphragm, said lines ensuring the feeding of the chamber with a constant fuel flow the pressure of which is solely dependent on the fuel density, and wherein the control valve comprises: - a cylinder and a slide gate mobile in translation within the cylinder, - an inlet orifice arranged in the cylinder and connected to the high-pressure line, - an outlet orifice arranged in the cylinder and connected to the low-pressure line, the control valve being conformed so that movement of the slide gate in the cylinder causes a variation in the fuel flow circulating from the inlet orifice to the outlet orifice, the slide gate comprising two movement-controlling end sections (320, 321), respectively connected to the high-pressure line and to an outlet of the metering element, and further comprising an additional movement-controlling section adapted to modulate the position of the slide gate as a function of the fuel density. - a fuel metering element, - a pump adapted to circulate a fuel flow towards the metering element, and - a control valve adapted to return, towards the pump, an excess fuel flow delivered to the metering element, as a function of a difference in fuel pressure at the terminals of the metering element, - a flow extraction line connecting the high-pressure line to a chamber of the control valve, said line comprising a pump adapted to deliver to said chamber a constant fuel flow at a pressure higher than the pressure of the fuel in the high-pressure line, and - a flow return line connecting the chamber to a fuel recirculation inlet of the high-pressure line, said line comprising a diaphragm, - a cylinder and a slide gate mobile in translation within the cylinder, - an inlet orifice arranged in the cylinder and connected to the high-pressure line, - an outlet orifice arranged in the cylinder and connected to the low-pressure line, the control valve being conformed so that movement of the slide gate in the cylinder causes a variation in the fuel flow circulating from the inlet orifice to the outlet orifice, the slide gate comprising two movement-controlling end sections (320, 321), respectively connected to the high-pressure line and to an outlet of the metering element, and further comprising an additional movement-controlling section adapted to modulate the position of the slide gate as a function of the fuel density.