Cloud storage solutions have gained momentum in recent years. However, cloud servers can not be fully trusted. Data access control have becomes one of the main impediments for further adoption. One appealing approach is to incorporate the access control into encrypted data, thus removing the need to trust the cloud servers. Among existing cryptographic solutions, Ciphertext Policy Attribute-Based Encryption (CP-ABE) is well suited for fine-grained data access control in cloud storage. As promising as it is, user revocation is a cumbersome problem that impedes its wide application. To address this issue, we design an access control system called DUR-CP-ABE, which implements identity-based User Revocation in a data owner Discretionary way. In short, the proposed solution provides the following salient features. First, user revocation enforcement is based on the discretion of the data owner, thus providing more flexibility. Second, no private key updates are needed when user revocation occurs. Third, the proposed scheme allows for group revocation of affiliated users in a batch operation. To the best of our knowledge, DUR-CP-ABE is the first CP-ABE solution to provide affiliation- based batch revocation functionality, which fits naturally into organizations' Identity and Access Management (IAM) structure. The analysis shows that the proposed access control system is provably secure and efficient in terms of computation, communi- cation and storage.