A fuel system for an internal combustion engine is provided, which comprises a first fuel tank, a fuel filter device, arranged between a low pressure pump operated by an electric motor and a high pressure pump, a first fuel conduit, through which the low pressure pump is arranged to supply fuel to the fuel filter device, and a control device, arranged in connection with an electric motor operating the low pressure pump. An overflow conduit is arranged in connection with a deaeration outlet, arranged in the fuel filter device and the first fuel tank, and the control device is arranged to control the electric motor, in such a way that the low pressure pump is active when the internal combustion engine is turned off for a limited period, whereby fuel may flow from the fuel filter device via the deaeration outlet and the overflow conduit, back to the first fuel tank.
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