Multi-entity cooperation in providing integrated medical and endowment service can fully stimulate the potential and vitality of service providers and accelerate resource sharing, and it is the basis of improving the service level and efficiency. Exploring how relationship capital can promote the formation of the service cooperation network for the integrated medical and endowment service is conducive to a deeper understanding of the service cooperation mechanism. It has theoretical value and policy significance for government departments, elderly care institutions, and medical institutions to gather together and promote the formation of a cooperative network. Based on typical cases, this paper uses grounded theory and qualitative comparative analysis (QCA) to analyze the formation path and specific effects of relationship capital to promote the integrated medical and endowment service cooperation network. It is found that there are multiple concurrent causal relationships between relational capital, situational conditions, trigger conditions, and the results of cooperative network formation. Multiple conditions promote the formation of cooperative networks through the combination and matching of government relational capital configuration, comprehensive relational capital configuration, and non-governmental relational capital configuration, which can produce recruitment effect, link effect, and catalytic effect respectively. From the perspective of expanding cooperative relationships, accumulating social relationship capital, and leveraging superior relationship resources, the dilemma of service cooperation can be overcome. At the same time, this conclusion emphasizes the important role of relationship capital in the field of public service governance in China, expands the research on the antecedent conditions of the public service cooperation network formation, and improves and develops the cooperative governance theory.