The purpose of this study is to identify the core competencies of graduate students at A research university in the context of graduate education in science and engineering, and to develop and validate a diagnostic tool to measure them. To achieve the research objectives, first, 6 factors and 18 sub-competencies of core competencies were derived based on a review of domestic and foreign studies, cases of excellent research-centered overseas universities, and interviews with members of A University. Second, a theoretical model was constructed by deriving behavioral indicators based on the core competencies and sub-competencies, and a preliminary survey was conducted on 188 graduate students of University A to verify the statistical validity of the theoretical model. Results of exploratory and confirmatory factor analysis, the core competencies of graduate students at A research university consisted of 6 factors, 16 sub-competencies, and 77 items. Specifically, it included “Independent research capability(13 items)”, “Social Entrepreneurship(10 items)”, “Academic agility(15 items)”, “Ingenious Challenges(15 items)”, “Collegial Collaboration(9 items)”, and “Mueunjae leadership(15 items)”. This study contributes to the development of theories related to core competencies of graduate students in science and engineering, and has practical significance as a basis for a data-driven competency-based graduate education system.