Identity-based revocation system (IBRS) generates the ciphertext with a revoked identity list such that only the non-revoked identities can use their private keys to decrypt this ciphertext. IBRS can be efficiently applied in some practical applications, such as the pay-TV systems when the number of revoked identities are much less than the non-revoked ones. However, since IBRS is based on identity-based cryptography, it also suffers from the inherent key escrow problem where the private key generator (PKG) has full control of each user's private key. As a consequence, it is hard to judge whether a pirated private key is generated by the PKG or the suspected user. There is no study on IBRS fulfilling accountability in literature to date. In this paper, we introduce the notion of accountable authority IBRS (A-IBRS), which provides accountability in IBRS schemes. In an A-IBRS, the aforementioned problem can be alleviated and resolved. Furthermore, a full black-box A-IBRS can distinguish the creator of a black box between the PKG and the associated user and the dishonest PKG is allowed to access the decryption results of the user private key. We formalize the definition and security models of the full black-box A-IBRS schemes. Then, we present a concrete full black-box A-IBRS scheme with constant-size master public key and private key. Finally, we prove the security of our scheme under the defined security models without random oracle.