The need of secure big data storage service is more desirable than ever to date. The basic requirement of the service is to guarantee the confidentiality of the data. However, the anonymity of the service clients, one of the most essential aspects of privacy, should be considered simultaneously. Moreover, the service also should provide practical and fine-grained encrypted data sharing such that a data owner is allowed to share a ciphertext of data among others under some specified conditions. This paper, for the first time, proposes a privacy-preserving ciphertext multi-sharing mechanism to achieve the above properties. It combines the merits of proxy re-encryption with anonymous technique in which a ciphertext can be securely and conditionally shared multiple times without leaking both the knowledge of underlying message and the identity information of ciphertext senders/recipients. Furthermore, this paper shows that the new primitive is secure against chosen-ciphertext attacks in the standard model.