With the exposure of security events in cloud storage, encrypting data before uploading has become the most favorable choice for cloud users, which makes search on encrypted data an important issue. Attribute-based encryption with keyword search (ABKS), which achieves data access control and search on encrypted data at the same time, has risen in response to the proper time and conditions. Traditional ABKS schemes are bounded to low efficiency and the security problem of Keyword Guessing Attack (KGA). We proposed a novel ABKS scheme named O2ABKS, which adopts the online/offline technique to enhance the efficiency, and designs an index generation mechanism that requires the private key of data owner to deal with the challenging concern of KGA. The scheme is proved to be IND-CKA and IND-KGA secure under the standard model. Compared with other schemes, our scheme is more expressive, efficient and applicable to cloud storage.