Keyword search on encrypted data allows one to issue the search token and conduct search operations on encrypted data while still preserving keyword privacy. In the present paper, we consider the keyword search problem further and introduce a novel notion called attribute-based proxy re-encryption with keyword search (ABRKS), which introduces a promising feature: In addition to supporting keyword search on encrypted data, it enables data owners to delegate the keyword search capability to some other data users complying with the specific access control policy. To be specific, ABRKS allows (i) the data owner to outsource his encrypted data to the cloud and then ask the cloud to conduct keyword search on outsourced encrypted data with the given search token, and (ii) the data owner to delegate other data users keyword search capability in the fine-grained access control manner through allowing the cloud to re-encrypted stored encrypted data with a re-encrypted data (embedding with some form of access control policy). We formalize the syntax and security definitions for ABRKS, and propose two concrete constructions for ABRKS: key-policy ABRKS and ciphertext-policy ABRKS. In the nutshell, our constructions can be treated as the integration of technologies in the fields of attribute-based cryptography and proxy re-encryption cryptography.