An exhaust gas cleaning system comprises a first sub system including a scrubber unit comprising a scrubber arranged to wash the exhaust gas with a scrubber fluid, and a centrifugal separator arranged in communication with the scrubber unit for receiving the scrubber fluid after washing and separate it into a first and a second fraction, which second fraction is more polluted than the first fraction. The exhaust gas cleaning system further comprises a second sub system including a membrane filter arranged in communication with the centrifugal separator for receiving the first fraction output from the centrifugal separator and separating it into a third and a fourth fraction, which fourth fraction is more polluted than the third fraction. A method for cleaning exhaust gas onboard a ship involves cleaning an exhaust gas onboard a ship.