In this paper, we present the notion of recipient-revocable identity-based broadcast encryption scheme. In this notion, a content provider will produce encrypted content and send them to a third party (which is a broadcaster). This third party will be able to revoke some identities from the cipher-text. We present a security model to capture these requirements, as well as a concrete construction. The ciphertext consists of k + 3 group elements, assuming that the maximum number of revocation identities is k. That is, the ciphertext size is linear in the maximal size of R, where R is the revocation identity set. However, we say that the additional elements compared to that from an IBBE scheme are only for the revocation but not for decryption. Therefore, the ciphertext sent to the users for decryption will be of constant size (i.e.,3 group elements). Finally, we present the proof of security of our construction.