Abstract: Attribute-based encryption (ABE), as a public key encryption, can be utilized for fine-grained access control. However, there are two main drawbacks that limit the applications of attribute-based encryption. First, as different users may have the same decryption privileges in ciphertext-policy attribute-based encryption，it is difficult to catch the users who sell their secret keys for financial benefit. Second, the number of resource-consuming exponentiation operations required to encrypt a message in ciphertext-policy attribute-based encryption grows with the complexity of the access policy, which presents a significant challenge for the users who encrypt data on mobile devices. Towards this end, after proposing the security model for online/offline traceable attribute-based encryption, we present an online/offline traceable ciphertext-policy attribute-based encryption scheme in prime order bilinear groups, and further prove that it is selectively secure in the standard model. If a malicious user leaks his/her secret key to others for benefit, he/she will be caught by a tracing algorithm in our proposed scheme. Extensive efficiency analysis results indicate that the proposed scheme moves the majority cost of an encryption into the offline encryption phase and is suitable for user encryption on mobile devices. In addition, the proposed scheme supports large universe of attributes, which makes it more flexible for practical applications.