Attribute-based encryption (ABE) is getting popular for its fine-grained access control in cloud computing. However, dynamic user or attribute revocation is a challenge in original ABE schemes. To address this issue, a new cipher text-policy ABE scheme with efficient revocation is proposed. In the new scheme, the master key is randomly divided into generating the secret key and delegation key, which are sent to the user and the cloud service provider, respectively. In our proposed scheme, the authority removes user's attribute without affecting other users' access privileges with this attribute. Finally, the scheme is proven selectively-structure chosen plaintext attack secure under the decisional q-Parallel Bilinear Diffie-Hellman Exponent (q-PBDHE) assumption. Compared with some existing schemes, our scheme has the lower storage overhead and communication cost.