Data integrity is a critical security issue in cloud storage. The data integrity checking schemes by a third-party auditor (TPA) have attracted a lot of attention. Sharing data among multiple users (uploaders) is an attractive feature of cloud storage. Considering the scenario of multiple uploaders, privacy-preserving cloud auditing makes it possible for the TPA to publicly verify the data integrity while guarantees that it cannot learn the identity of the data uploader. In this paper, we propose a (t, n)-threshold privacy-preserving auditing scheme. Every user could generate a tag piece of a message from the tag generation algorithm individually. To respond a challenge from the TPA, the server needs at least t tag pieces from different users among all n users. Our scheme does not resort to ring signature or group signature techniques. The tag of a message consists of only one element, which is independent of the number of the users within the group. Therefore, the efficiency of tag generation and auditing of our scheme is compatible with an efficient construction (Wu et al., in: International conference on information security practice and experience ISPEC 2016, Springer, New York, 2016). We use the pairing-based cryptography library (PBC library-0.5.14) to implement the scheme and compare both the computation and transmission cost of our scheme with some existing schemes.