Adopting the grounded theory research method, this paper conducts an in-depth analysis of 11 international library artificial intelligence (AI) governance policy texts, clarifies the structural elements of the AI governance process in international libraries, and constructs a framework model of this governance process by integrating the common characteristics of the policy texts. Based on this, it puts forward implications for the application governance of AI in libraries in China. The research finds that AI governance in international libraries consists of four components: governance subjects, governance objects, governance principles, and governance activities. It forms a top-down hierarchical governance route, including positive "incentive governance-enabling governance-integrated governance" and negative "preventive governance-regulatory governance-protective governance". This study provides reference value for the practice of AI governance in Chinese libraries.