Focusing on the large decryption overhead of the data user and the lack of effective attribute revocation of the Multi-Authority Attribute-Based Encryption (MA-ABE) access control scheme in cloud storage, an attribute revocation and verifiable outsourcing supported multi-authority attribute-based encryption scheme was proposed. Firstly, the data user's decryption overhead was markedly reduced and the integrity of the data was verified by using verifiable outsourcing technology. Then, the bilinear mapping was used to protect the access policy, preventing the identity of the data owner from leaking. Finally, the version key of each attribute was used to realize the immediate attribute revocation. The security analysis shows that the proposed scheme is safe under the decisional q-bilinear Diffie-Hellman exponent assumption in the standard model, achieves forward security and is able to resist collusion attack. The performance analysis shows that the proposed scheme has great advantages in terms of functionality and computational cost. Therefore, this scheme is more suitable for multi-authority attribute-based encryption environment in cloud storage.