"Double first-class" construction is a top-level design of advanced education under the new historical conditions which aims to improve the development level of higher education in China. Mid-western regional universities are an indispensable part of higher education in China. Under the background of "double first-class" construction, there are still many problems in the existing ways of postgraduate education in mid-western regional universities. In order to cultivate more high-level composite talents who can well serve scientific research innovation and regional economic construction, mid-western regional universities should take advantages of "double first-class" construction to promote the reform of postgraduate education in terms of internationalization, team building, resource allocation and innovative curriculum system construction. This paper closely follows the overall situation of colleges and universities in Jiangxi Province, and takes the graduates education in some universities as an example. Problems existing in postgraduate cultivation of mid-western regional universities under the background of "double first-class" construction are summarized. To solve these problems, measures for reforming postgraduate cultivating way and scheme are proposed. The research outcomes can provide references for promoting the cultivation quality of postgraduate students in mid-western regional universities.