An auditing scheme is a good way to prove owner’s data outsourced to the cloud are kept intact, and a scheme capable of giving public verifiability service is a good option that some researchers have managed to build for the last few years. However, in a public auditing scheme everybody does verification of data and a possibility of leaking some secrete information to the public verifiers is an issue that data owners are unhappy with this scenario. For example, the data owner does not want anybody else to know he has the data stored in the cloud server. Motivated by the issue of privacy associated with public auditing system, we proposed a designated verifier auditing (DVA) scheme based on Steinfeld et al.’s universal designated verifier (DV) signature scheme. Our DVA scheme authorizes a third party auditor with private verification capability. It provides private verification because the scheme involves private key of the verifier. Moreover, we present the batch auditing scheme to improve auditing efficiency. Through rigorous security analysis we showed that our scheme is provably secure in the random oraclemodel assuming that the computational Diffie-Hellman (CDH) problem is hard over the group of bilinear maps.