Data security is the most important feature for accessing data in the cloud. Due to data outsourcing and distrust cloud servers, the data access control becomes a challenging issue in cloud storage systems. Cipher text-Policy Attribute-Based Encryption (CP-ABE) is regarded as one of the most suitable technologies for data access control in cloud storage, because it gives data owners more direct control on access policies. However, it is difficult to directly apply existing CP-ABE schemes to data access control for cloud storage systems because of the attribute revocation problem.