A mooring system for mooring a turreted vessel off-shore, which comprises: line pulling equipment mounted in the vessel turret; a block located in the water at a depth below expected wave action and at a distance from the vessel; a mooring line extending from the puling equipment, through a fairlead at the bottom of the vessel turret, through the block and back for releasable attachment to the vessel; and mooring tackle attached to the block and extending away from the vessel to an anchor. The mooring line and mooring tackle form a catenary between the vessel and the anchor which has a curve adapted to maintain the anchor securely attached to the sea bottom, and to maintain the block below the depth of expected wave action.