Celestial navigation is an important type of autonomous navigation technology which could be used as an alternative to Global Navigation Satellite Systems (GNSS) when a vessel is at sea. After several centuries of development, a variety of astronomical vessel position (AVP) determination methods have been invented, but the basic concepts of these methods are all based on angular observations with a device such as a sextant, which has disadvantages including low accuracy, manual operation, and a limited period of observation. This paper proposes a new method that utilises a fisheye camera to image the celestial bodies and horizon simultaneously. Then, we calculate the obliquity of the fisheye camera's principal optical axis according to the image coordinates of the horizon. Next, we calculate the altitude of the celestial bodies according to the image coordinates of the celestial bodies and the obliquity. Finally, the AVP is determined by the altitudes according to the robust estimation method. Experimental results indicate that this method not only could realize automation and miniaturization of the AVP determination system, but could also greatly improve the efficiency of celestial navigation.