With the development of database-as-a-service (DaS), data in cloud is more interesting for researchers in both academia and commercial societies. Despite DaS’s convenience, there exist many considerable problems which concern end users about data loss and malicious deletion. In order to avoid these cases, users can rely on data auditing, which means verifying the existence of data stored in cloud without any malicious changes. Data owner can perform data auditing by itself or hire a third-party auditor. Until now, there are two challenges of data auditing as the computation cost in case of self auditing and data privacy preservation in case of hiding an auditor. In this paper, we propose a solution for auditing by a third-party auditor to verify data integrity with efficient computation and data privacy preservation. Our solution is built upon cryptographic hash function and Chinese Theorem Remainder with the advantage in efficient computation in all three sides including data owner, cloud server, and auditor. In addition, the privacy preservation can be guaranteed by proving the third-party auditor learns nothing about user’s data during auditing process.