The Industrial Internet of Things (IIOT) contains many devices from different autonomous domains (e.g., factories), which need to cooperate to complete complex manufacturing process. Devices from different domains collaborate with each other, which greatly raises trust concerns about device-to-device interactions. Existing trust management approaches may result in the risk of privacy leakage and low accuracy of trust evaluation. Thus, trust issues during interaction remain unsolved but imperative. In this paper, we propose a blockchain-based privacy-preserving trust management architecture PPTMA. Specifically, PPTMA adopts federated learning to train a task-specific trust model for different collaborative task. Our work is the first attempt to research the relationship between the weight calculation of trust metric and the change of context in the field of trust management. To preserve the privacy of devices, differential privacy (DP) is exploited during the trust evaluation process. In addition, a game theory-based incentive mechanism is proposed to encourage the IIOT device for actively and honestly submitting the trust data into the blockchain as so to promote the accuracy of trust computing. Finally, we also design a parallel consensus protocol (OPBFT) which realizes an assembly line to speed up the efficiency of the consensus process. The idea of consensus assembly line firstly proposed by us brings new opportunities for improving the consensus efficiency. Extensive experiments have been conducted to show the effectiveness and efficiency of the proposed method.