A system and method for metering fuel is provided which includes a fuel supply line and a metering valve in fluid connection with the fuel supply line to control a flow of fuel through the fuel supply line. The valve is movable into a closed position to block a primary flow of fuel and create a leakage fuel flow in the fuel supply line downstream of the metering valve. The system also includes a venturi apparatus fluidly coupled to the fuel supply line upstream of the metering valve. The venturi apparatus is further coupled to the fuel supply line downstream of the metering valve to direct the leakage fuel flow out of the fuel supply line.