China is in the decisive stage of building a moderately prosperous society at present. Realizing the modernization of higher education basically is an important content of building a moderately prosperous society. Modern higher education plays an irreplaceable role in improving China's comprehensive national strength and realizing the great rejuvenation of the Chinese nation. Graduate education is the highest level of China's higher education, which bears the historical responsibility of training high-level talents for the development of national economy. At present, the country is vigorously advancing the modernization of higher education. Research on the cultivation of core qualities of graduate students is not only an implementation and inheritance of quality education, but also an urgent need to improve the quality of graduate education and build double top universities. This paper analyzes the feasibility of cultivating the core quality of Postgraduates under the background of the modernization of higher education, expounds the basic characteristics of graduate students' core literacy, and puts forward some suggestions on how to cultivate the graduate students' core literacy on this basis.