China's 7000 m manned submersible JIAOLONG carried out an exploration cruise on the Indian Ocean Ridge from late 2014 to early 2015. During the cruise, the submersible completed manned diving in situ investigations into hydrothermal vents in the area. One of the primary tasks of the work was to map the vents precisely. In this paper, we briefly introduce the cruise, and then focus on the submersible's underwater navigation and the positioning of five hydrothermal vents using the Ultra-Short Base Line positioning system of JIAOLONG. This study describes the positioning data of each vent from different dives, and discusses the variation in the positioning data among dives in the same location. We propose a shape based calibration method using the trajectories of the submersible and its mother ship to correct for noted deviations in position data. This method is verified using calibration results of five typical vents and provides a promising technique that can be used for other underwater vehicles under similar conditions.