Aiming at theoretical mathematics major and taking topology major graduate training as an example, this paper aims to discuss how to build a set of graduate training model that can not only consolidate the foundation of topology major, but also lead the interdisciplinary research in the information field in the current era of big data. By reviewing the historical development of topology and its status in modern science, this paper analyzes the current situation and existing problems of graduate education in topology, and combines traditional and innovative teaching methods to put forward a set of graduate training model from "laying professional foundation" to "leading cross-research". Furthermore, this paper elaborates the importance of relevant interdisciplinary research in the field of topology, as well as the various directions and successful cases of cross-research at present. Finally, by summarizing the research experience and shortcomings, suggestions and prospects for the future graduate education of topology are put forward. This study is of great significance for guiding the postgraduate educators in the field of topology and related theoretical mathematics.