"Double first-class" construction is a major strategic deployment of our party and country in the new historical conditions which is an effective approach to promote the development of higher education and deepen the reform of higher education system in China. We should adhere to the guiding ideology of "four actions" and elimination of "five only". According to the general policy of postgraduate education reform in China, this paper analyzes the current situation of doctoral cultivation and degree granting in universities which under the background of “double first-class” construction. In view of the shortcomings of the traditional education and evaluation methods, this paper clarifies the reform ideas of paying attention to the process supervision and paying attention to the diversification of evaluation methods to establish and improve the evaluation system reform of doctoral students' innovation achievements under the background of "double first-class". In order to establish and improve the reform of doctoral candidates innovation achievement evaluation system, the universities should promote the reform in terms of Building a first class doctoral teaching staff, improving the management system, supervision mechanism of doctoral thesis quality and formulating the corresponding innovation achievement evaluation scheme according to the characteristics of different universities and disciplines. The relevant reform measures proposed in this paper and the research outcomes can provide references for the cultivation and degree granting of doctoral candidates in universities.