In order to solve the problems of high computational cost of Attribute-Based Encryption （ABE） scheme and low efficiency of data search in cloud servers simultaneously， an Outsourced Attribute-Based Encryption scheme with Keyword Search （OABE-KS） was proposed. Firstly， the outsourced computation technology was used for reducing the local computing cost of encryption and decryption users to the constant level. Then， the indexes and trapdoors of the corresponding keywords were generated by the encryption user and the decryption user respectively， and the cloud server was used to match them. After that， the successful matching results would be returned to the decryption user by the cloud server. The adaptive security of the proposed scheme was proved under the composite order group. According to the experimental analysis， when the number of attributes changes from 10 to 100， the running time of each stage of the proposed scheme is basically unchanged， showing that the running time of the proposed scheme in each stage does not vary with the number change of attributes. Experimental results show that， the proposed scheme is suitable for the application on resource-limited devices and is not affected by the number of attributes in practical applications.