With the rapid increase of the industrial data and the development of the industrial Internet of Things (IIoT) paradigm, the efficiency and the quality of service of the emerging applications have been improved. However, the contradiction between data sharing and privacy preserving is still an obstacle in the IIoT. To this end, in this article, we propose a privacy-preserving and publicly auditable multiparty computation scheme for industrial data sharing and computing, which avoids privacy leakage and computation misbehavior by separating the data ownership, data use, and data verification. Using the blockchain technology, a transparent management platform is provided to recognize and trace the illegal data and computation behavior. Moreover, we integrate the noninteractive zero-knowledge proof in the multiparty interaction mechanism, wherein the verification of data consistency and computation validity is executed publicly on the blockchain. Finally, we implement experiment to evaluate the performance of the computation latency, communication overhead and the influence of encryption parameter, and the numerical results illustrate the efficiency and feasibility of our scheme.