Geometric positioning methods for earth remote sensing images cannot be used for Chang’E-3 (CE-3) moon-based Extreme Ultraviolet Camera (EUVC) images because of lack of control points. According to this present situation, working principle and related coordinate systems for EUVC were introduced, and a geometric positioning algorithm was proposed for EUVC observations based on telemetry parameters and strict coordinate transformation relationship. Algorithm of geometric positioning was researched and positioning accuracy was evaluated. The results show that the space pointing of EUVC optical axis and CE-3 lander’s position in Solar Magnetic System at image acquisition epochs can be calculated by the proposed algorithm for high-precision geocentric position. Geocentric position results can also be used to correct the original images to ensure the reliability of the EUVC observations and to realize CE-3’s scientific objective of the space environment detection.