Abstract: With the wide use of the cloud storage service, user data is not only stored in the cloud, but also shared among multiple users. To ensure the integrity of the shared data in the cloud, the researchers have proposed many public auditing schemes for group shared cloud data. However, the existing schemes just consider that the group users only include a single group manager without considering that multiple group managers may exist in a group simultaneously and the problem of frameability when tracing the real identity of the group user is also not taken into account. The proposed scheme gives the first public auditing security model for a group shared data with multiple managers, and constructs homomorphic authenticable group signature with multiple group managers based on revocable group signature and (t,s) secret sharing scheme, and designs the first public auditing scheme for a group shared data with multiple managers. The proposed scheme not only can achieve multi-levels privacy-preserving abilities like identity privacy, traceability and non-frameability, but also can well support group user revocation and resuming. Moreover, the overhead of the auditing does not grow with the number of the group uses, which ensures the feasibility and the efficiency of the scheme.