In order to solve the problems of collusion attack and multidomain shared data in the multiauthority attributebased encryption scheme, we present a multidomain access control scheme based on multiauthority attribute encryption for cloud storage. In the proposed scheme, the central authority does not participate in the generation process of users' key, which can effectively avoid the attack between users and authorized institutions. To achieve single domain and multidomain data sharing, the cloud server utilizes the linear secret sharing scheme and the proxy reencryption technique to reencrypt the data files. Our analysis shows that the proposed scheme has satisfactory performance in key generation and file encryption & decryption. Furthermore, this scheme is adaptively secure under the qparallel BDHE assumption.