In this work, we design a new attribute-based encryption scheme with the revocation capability. In the proposed schemes, the user (broadcaster) encrypts the data according to an access policy over the set of attributes, and a list of the identities of revoked users. Only recipients who have attributes which satisfy the access policy and whose identity is not in the list of revoked users will be able to decrypt the message.The proposed scheme can be used for revocation of up to t users. The complexity of proposed schemes is dependent on the number of revoked users r, rather than on the total number n of users in the system. The security of the scheme has been proved under the Decisional Bilinear Diffie-Hellman (DBDH) assumption.