With the rapid development of digital economics, a large number of data have been accumulated in the supply chain system, and data islands have appeared. Data sharing is an imperative way to unlock the data value of a supply chain system. A safe and effective access control mechanism for privacy-sensitive data is key in data sharing. At present, traditional access control mechanisms are static, single-factor control, and prone to a single point of failure. For dealing with these, a fine-grained access control (FGAC) framework for supply chain data sharing is proposed, based on the blockchain Hyperledger Fabric. It augments role-based access control (RBAC) by giving different attribute keywords to different types of users. This framework is implemented in smart contract Chaincodes and quantitatively verified by using the model-checking tool UPPAAL. The experiment results show that the FGAC framework enhances the efficiency and safety in the process of data sharing for the supply chain system, compared with the existing works.