In this paper, the goodness-of-fit test (GFT) method for estimating the minimum magnitude of completeness (MC) is introduced first and then applied to determine the temporal-spatial distribution of MC of the Longmenshan fault zone, Sichuan Province, and its surrounding area. Finally, advantage and problems of the method in application are summarized and discussed. The study suggests that based on the assumption that the G-R relationship has the power-low distribution, the GFT method is used to estimate a minimum magnitude of completeness MC through fitting a G-R relationship for a set of observed data by adjusting various minimum magnitudes gradually from small to big ones and eventually taking that minimum magnitude when the fitted G-R relationship can match best the set of observed data to be the result.