Social Internet of Things (SIoT) integrates the social concept into the Internet of Things (IoT) for enhancing the efficiency of services. Due to the increasing scale of the network and the intellectualization of IoT objects, the development of SIoT has also been accompanied by the issue of trust management which is crucial to the security and reliability of the system. The definition and evaluation of the trustworthiness of objects are vital to build cooperation among objects. In this paper, we employ the blockchain technology to address the trust management issue in SIoT. Blockchain will be adopted as an underlying support technology for trust-related data storage and retrieval. Moreover, we present a flexible and adaptive trust computation method to enhance the reliability of objects’ trustworthiness evaluation. The simulated experiment results demonstrate that the proposed blockchain-based method enhances the effectiveness and security of trust management in SIoT.