For securing confidential applications such as credit card transactions, on-line auctions and business contract signing, etc., a convertible authenticated encryption (CAE) scheme simultaneously satisfying the properties of authenticity, confidentiality and non-repudiation is a better choice. By combining the advantages of identity-based systems and key-insulated ones, in this paper, we propose the first novel identity-based key-insulated CAE (IB-KICAE) scheme from pairings. Integrating with key-insulated systems, our scheme can effectively mitigate the impact caused by key exposure, as each user can periodically update his private key while the corresponding public one remains unchanged. The proposed scheme is conversion-free and supports unbounded time periods and random-access key-updates. Moreover, to guarantee its practical feasibility, the essential security requirement of confidentiality against indistinguishability under adaptive chosen-ciphertext attacks (IND-CCA2) and that of unforgeability against existential forgery under adaptive chosen-message attacks (EF-CMA) are realized in the random oracle model.