To address the problem of how to authenticate a valid authority in the real life, a new ciphertext-policy attribute-based encryption scheme with verifiability on authority is proposed. By employing ring signature technology, multiple authorities are organized into a valid organization, and the value of ring signature which can be used to prove the legitimacy of each authority is reasonably embedded in the user's private key, so that users are able to verify the validity of the authority. In addition, the linear secret sharing scheme is adopted to support any monotone access structures in our scheme, and it is proved to be full security based on the difficult assumptions on the composite order group under the standard model. Finally, compared with some related attribute-based encryption schemes, the proposed scheme has certain performance advantages in terms of ciphertext size, user's private key size, bilinear pairing calculation and so on. Therefore, it is more suitable for cloud environment and resource-limited mobile devices.