Online social networks (OSNs) are nowadays an important field of applications thanks to the recent surge in online interaction. However, the illegal disclosure of user's private data can cause damaging consequences and even threaten the safety of users' life. The privacy issues of OSNs have become a matter of great concern for many people. In recent years, there are some research works to address this privacy issue, yet they do not always focus on providing the normal social network services for users, such as data sharing, data retrieval and data access services. Therefore, it is a challenge to ensure the security of sensitive data while providing efficient and privacy-preserving social network services for users. In this paper, we propose a novel blockchain-based privacy-preserving framework for online social networks, called BPP. Combined blockchain and public-key cryptography technique, the BPP framework can achieve secure data sharing, data retrieving, and data accessing with fairness and without worrying about potential damage to users' interest. Specifically, based on blockchain and public key encryption with keyword search technique, a secure, fair and efficient keyword search algorithm is proposed, with which the BBP framework realises privacy preservation of user's query and then obtain accurate query results with assurance and without needing for any further verification operation in online social network. Finally, we implement a prototype of our framework and deploy it to a locally simulated network. The extensive experiments and security analysis demonstrate the security, efficacy and efficiency of our proposed framework.