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In this paper, we propose the concept of identity-based anonymous designated ring signature. This concept extends the existing notion of ring signatures in two ways: firstly, it allows a member from the ring to sign a message directed to a designated verifier, but secondly, we would like to have an anonymous designated verifier. At a glance, these two additional properties seem contradictory, but we shall show an example of a situation where this kind of primitive is required. We present a formal model of such a scheme and proceed with a construction based on bilinear pairings. Our scheme is provably secure under the random oracle model. We also present an extension of this concept, namely convertible identity-based anonymous designated ring signatures that allow the signer to prove the ownership of the signature, if necessary.