In a secure data sharing system, users can selectively retrieve encrypted files by performing keyword search over the ciphertext of data. Most of the existing searchable encryption schemes can provide security protection for both data owner and users. Nevertheless, three pivotal issues need to be addressed. Firstly, the cloud might return a wrong result or incomplete result for some reasons, e.g., saving the computing resources. Secondly, users need to store massive keys to generate trapdoors and decrypt the ciphertext of data, which brings great challenges to users' key management. Thirdly, when users perform keyword search over a large number of files, they need to generate and submit massive trapdoors, which is unrealistic. Proceeding from these points, in this paper, we propose an efficient verifiable key-aggregate keyword searchable encryption (EVKAKSE) scheme. In this scheme, the data owner distributes only one aggregate key to users for keyword search, decryption and verification, who can use the aggregate key to generate a single trapdoor for keyword search over shared files. Generally, we define the requirements of the scheme, analyze the threat models and give a valid construction. Furthermore, our security analysis and experimental evaluation demonstrate that the scheme is efficient and secure.