Vessel (1) with mooring system, comprising a turret (3) anchored to the seabed and a turret casing (5) being part of the vessel, wherein the turret (3) and turret casing (5) are interconnected by a connecting element (6) comprising a bearing arrangement (7) and wherein the connecting element (6) has a first end connected to the turret casing and an opposite second end connected to the turret. The connecting element (6) is positioned in such a manner that it experiences tensile forces. When the turret (3) downwardly loads the turret casing (5) the first end of the connecting element (6) is positioned at a higher level then the second end thereof. When the turret (3) upwardly loads the turret casing (5) the first end of the connecting element (6) is positioned at a lower level then the second end thereof.