A ship flue gas scrubbing apparatus and scrubbing method are provided. The apparatus includes a housing, an upper scrubbing layer at the upper side inside the housing, and a liquid collecting pool in the lower side inside the housing, a flue gas leading-in port between the scrubbing layer and the liquid collecting pool, a scrubbing seawater inlet above the scrubbing layer, and a cooler located at a flue gas passage between the flue gas inlet outside the housing and the scrubbing layer. The method includes leading flue gas, cooling, injecting scrubbing seawater, scrubbing and other steps.