To meet the higher demands of the earth and space observation, the aperture of space telescope mirror has took step to 10 m order of magnitude from 1 m with an ever-increasing trend. As a key technology for the space telescope, the large aperture mirror support is related directly to the surface shape accuracy and stability of the mirror, and crucial to the actual observation ability and even the success of the telescope mission. Three main forms of mirror support were discussed and their applicability were compared. The influential factors on the mirror mount design were summarized and based on this summary some key points and principles for support design were discussed. Combined with analysis on support technique research progress at home and abroad, the key techniques such as optimization on the number and location of support points, athermal design and un-stressed assembly and the trend of development were scrutinized. It is expected to provide reference for large space telescope of our country and thus promote leapfrog development in the new round of space exploration.