An Extreme ultraviolet (EUV) Camera was installed onboard the Chinese lunar surface landing mission, the Chang'E-3 lander, as a useful method to observe the Earth plasmasphere. This EUV optical payload obtained more than 600 moon-based Earth plasmasphere images since December 14, 2013. However, due to errors of unknown size and origin in the platform attitude control of the lander and in the EUV telescope pointing control during the mission operating periods, the geocentric coordinates in these EUV images are not fixed in the same position of CCD pixel. Before adequately calibrating, these positioning offsets will introduce extra errors into the analysis of the plasmaspheric structure. With only a little insufficient telemetry information, an effective calibrating method of circle-based differential algorithm is suggested and demonstrated, for automatically and precisely detecting the geocentric position in each EUV image of Chang'E-3 mission. In each EUV image, the tested method uses the outline of a circle as the basic unit to capture the contour for the bright region based on the spectral characteristic. Then, the center of the extracted circle is adopted as the geocentric position for the image. The preliminary analysis shows that this method can effectively detect the geocentric position being always consistent with the recognition result by the basic hand labor method. It is found that the radius of the circles varies from month to month from December, 2013 to May, 2014. The monthly averages of radius show relative notable positive correlation and negative correlation with the changes of both Zenith angle of the Earth at the landing area of Chang'E-3 lander, and B C. Zheng the Earth-moon distance, respectively. This method and results here will benefit the Chang'E-3 EUV study.