Benefited from cloud computing, users can achieve an effective and economical approach for data sharing among group members in the cloud with the characters of low maintenance and little management cost. Meanwhile, it must provide security guarantees for the sharing data files since they are outsourced. Unfortunately, because of the frequent change of the membership, sharing data while providing privacypreserving is still a challenging issue, especially for an untrusted cloud due to the collusion attack. Moreover, for existing schemes, the security of key distribution is based on the secure communication channel, however, to have such channel is a strong assumption and is difficult for practice. In this paper, a secure data sharing scheme for dynamic members was proposed. Firstly, a secure way for key distribution without any secure communication channels, and the users can securely obtain their private keys from group manager was proposed. Secondly, this scheme can achieve fine-grained access control, any user in the group can use the source in the cloud and revoked users cannot access the cloud again after they are revoked. Thirdly, the scheme from collusion attack, which means that revoked users cannot get the original data file even if they conspire with the untrusted cloud was protected. In the proposed scheme, by leveraging polynomial function, a secure user revocation scheme was achieved. Finally, this scheme can achieve fine efficiency, which means previous users need not to update their private keys for the situation either a new user joins in the group or a user is revoked from the group. The results will show effectiveness of the scheme for potential practical deployment, especially for big data deduplication in cloud storage.