The scheme proposed by Zhou et al. (ZHOU M, MU Y, SUSILO W, et al. Privacy enhanced data outsourcing in the cloud. Journal of network and computer applications, 2012, 35(4): 1367-1373) was analyzed, and the shortcoming of no access privilege revocation was shown. To address the shortcoming, an outsourced data encryption scheme with revoking access privilege was proposed. Firstly, the data were divided into several data blocks, and each data block was encrypted separately. Secondly, with the key derivation method, the number of keys stored and managed by the data owner was reduced. Finally, multiple decryption keys were constructed on an encrypted data to revoke access privileges of some users, without affecting the legitimate users. Compared with Zhou's scheme, the proposed scheme not only maintains the advantage of privacy protection to the outsourced data in the scheme, but also realizes access privilege revocation for users. The analysis results show that the proposed scheme is secure under the assumption of the Discrete Logarithm Problem (DLP).