Abstract: The Moon-based ultraviolet telescope (MUVT) is one of the payloads on the Chang'E-3 (CE-3) lunar lander. Because of the advantages of having no atmospheric disturbances and the slow rotation of the Moon, many scientific researches which cannot be completed on Earth can be carried out by MUVT such as making long-term continuous observations of a series of important celestial objects in the near ultra-violet band (245~340 nm) Geometric positioning of MUVT observation data is crucial for the successful implementation of moon-based astronomical observations, which is one of scientific objectives of China's second phase lunar exploration mission, by accurately obtaining the celestial coordinates of each star image in the telescope images. In this paper, working principle and related coordinate systems for MUVT of CE-3 lander will be introduced. Then the algorithm of geometric positioning for MUVT observations will be researched and the positioning accuracy will be evaluated. The results show that high-precision astronomical coordinates within 0.2° can be obtained by the geometric positioning algorithm studied in this paper.