The invention relates to a vessel (1), especially a drillship or so-called drilling ship. The vessel comprises a hull (3) having a bottom surface (5) and a deck (7). Said vessel is provided with a moon pool (2), which extends from said bottom surface of the hull in an upward direction through the hull. Further, said vessel is provided with a cavity (10) located at a front side of the moon pool. Said cavity is at least partly open at a bottom side thereof in order to allow water to flow into said cavity. Moreover, said cavity is at least partly open at a rear side of said cavity in order to allow water to flow directly from said cavity into the moon pool, as a result of which moon pool sloshing can be diminished and the mean flow resistance of the vessel when sailing can be reduced.