Group signature can provide the privacy-preserving authentication mechanism for the blockchain. In the traditional blockchain privacy-preserving scheme based on the group signature, there is only one group manager to revoke the anonymity. Thus, the traditional scheme will have single point of failure and key escrow problems. To solve these problems, we propose a privacy-preserving scheme in the blockchain based on the group signature with multiple managers. Our scheme is constructed based on bilinear pairing and the technique of distributed key generation. Finally, we analyze the application of the proposed scheme in the field of blockchain-based provable data possession (PDP), as well as the correctness and security of the scheme.