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Research learning engagement is the basic element of master’s students’ innovation output, and the supervisor is the first responsible body for master’s students’ cultivation. Exploring the influence of the supervisor–postgraduate relationship on master’s students’ research learning engagement, with a focus on the mediating role of academic aspiration, is of great significance for the improvement of master’s students’ cultivation quality. We surveyed 569 master’s students at a university in Wuhan, China, using 3 measurement tools: the Supervisor–Postgraduate Relationship Scale, the Research Learning Engagement Scale, and the Academic Aspirations Scale. The results showed that: (1) The supervisor–postgraduate relationship positively and significantly predicted master’s students’ research learning engagement, and academic aspiration played a fully mediating role in the process. (2) There were differences in the effects of the three dimensions of the supervisor–postgraduate relationship on master’s students’ research learning engagement, with research collaboration having the greatest total effect on the impact of master’s students’ research learning engagement. This study emphasizes the importance of the supervisor–postgraduate relationship and academic aspirations and provides some implications for improving the research learning engagement of master’s students.