In this abstract, we first propose a revocable multi-authority CP-ABE scheme, where an efficient and secure revocation method is proposed to solve the attribute revocation problem in the system. Our attribute revocation method is efficient in the sense that it incurs less communication cost and computation cost, and is secure in the sense t hat it can achieve both backward security (The revoked user cannot decrypt any new ciphertext that requires the revoked attribute to decrypt) and forward security (The newly joined user can also decrypt the previously published ciphertexts, if it has sufficient attributes). Our scheme does not require the server to be fully trusted, because the key update is enforced by each attribute authority not t he server. Even if the server is not semi-trusted in some scenarios, our scheme can still guarantee the backward security. Then, we apply our proposed revocable multi-authority CP-ABE scheme as the underlying techniques to construct the expressive and secure data access control scheme for multi-authority cloud storage systems. The analysis and simulation results show that our proposed data access control scheme is secure in the random oracle model and is more efficient than previous works.