In recent years, with the further improvement of mobile devices’ performance and the rapid development of mobile Internet, more and more mobile terminals participate in cloud data storage and data sharing. In order to support mobile devices with constrained resource effectively in terms of sharing data safely and efficiently in the cloud, a secure and efficient attribute-based encryption scheme with keyword search (ABKS) is proposed in this paper. The proposed scheme is based on the AND gate access structure with wildcards, which is proven to be IND-CKA (indistinguishable against chosen keyword attack) secure and achieves keyword security under the standard model. The scheme adopts the Viète’s formulas to make each attribute only be represented by one element, and the length of index is constant, the length of trapdoor and secret key and the computation complexity of trapdoor algorithm and search algorithm grow linearly with the maximum number of wildcards that can be used in the access structure, in addition, the scheme removes the secure channel, which reduces the communication overhead further during the transmission process of index and trapdoor. Efficiency analysis shows that compared with other schemes, the proposed scheme has less computation overhead and communication overhead, which is more suitable for mobile cloud storage environment.