Abstract: Cloud storage, as a novel data storage architecture, has been widely used to provide services for data draw to store and share their data in cloud. However, the security concerns of cloud storage also draw much attention of the whole society. Since some cloud service providers are not trustworthy, the data stored in their cloud servers could be stolen or accessed by unauthorized users. Ciphertext-policy attribute based encryption (CP-ABE) can be used to solve such security problems in cloud, which can encrypt data under a specified access policy thus to maintain data confidentiality as well as access control. Unfortunately, traditional CP-ABE schemes suffer from key escrow problems and are lack of policy update. In this paper, we propose a new multi-authority CP-ABE scheme with policy update, which can efficiently cut down the computation cost and communication cost compared with other schemes in literature. We also prove the semantic security for our scheme, and also analyze its efficiency.