A method and a system are provided for the safe berthing of marine vessels in the high seas and other unprotected open waters. The invention allows a large vessel to be berthed alongside in close enough proximity to a marine structure so that conventional loading arm equipment may be used to load and unload the vessel under most environmental conditions. One or more floating dolphins moored to the bottom of the sea and provided with fendering means are used for berthing the vessel alongside to the marine structure. The preferred type of floating dolphin is a triangular semi-submersible moored buoyant structure comprising three buoyant column members, or "caissons", arranged invertical fashion, three buoyant hull segments, or "pontoons", that support and separate the column members and provide heave damping to the moored buoyant structure, and three horizontal bracing members that retain the tops of the column members in place.