An improved mooring system for a vessel (10) having a mooring turret (19) which is rotatably coupled to a well (14) of the vessel (10) such that the vessel (10) is free to weathervane about the mooring turret is disclosed. An anchor leg support base (18) is fixed with the mooring turret (19) with anchor lines (20) secured thereto and anchored to the sea floor (24). A riser turret (25) is rotatably coupled to the mooring turret (19) and is fixed to the well (14) of the vessel. A riser support base (100) is pivotally coupled to a riser support device (30) for mounting the upper ends of a plurality of flexible risers (48) extending from the sea floor. The riser mounting device (30) is arranged and designed to pivot about two axes (34, 40) at right angles to each other relative to the riser support base (100). The gimbaled riser mounting device (30) provides a generally uniform load distribution among the risers (48) upon twisting or bundling of the risers (48) which result from weathervaning of the vessel (10) about the mooring turret (19).