The trust system is widely used to prevent malicious behaviors, and it is a key element for vehicles to establish interactions in the Internet of Vehicles (IoV). Nevertheless, trust and privacy remain unresolved concerns stemming from the distinctive features of the IoV. The IoV must thwart malicious attackers from spreading false data while ensuring that the vehicle’s evaluation data is not leaked, which is of utmost importance. In this paper, we propose a blockchain-based trust model (BPS-V), which supports ciphertext computation of trust evaluation data submitted by different vehicles. Design a cooperative update method for vehicle trust, which utilizes an improved distributed two-trapdoor public-key cryptography algorithm to achieve cooperative computing of trust and reduce the risk of privacy leakage of evaluation data. On this basis, BPS-V introduces blockchain sharding technology to realize cross-domain storage and sharing of the trust. Simulation results show that our scheme can effectively protect the privacy of evaluation data and maintain a high detection rate and low false alarm rate in different road environments. Compared with traditional schemes, BPS-V can improve the efficiency of trust updates and the detection of malicious vehicles by 9.5% and 32%.