In the designated verifier signature, the validity of signature can be proved by the specific verifier although the verifier has no ability to prove this to others. On the other hand, strong designated verifier signature (SDVS) can only be verified by the designated verifier. It will not be verified without the designated verifier's private key. The third party cannot tell who generates the signature. Even if the true signer signs a message by using SDVS, he has no ability to show any evidence. In some cases, the true signer wants to admit the signature if the admission can bring about reward. On the basis of the idea, this paper proposes the new concept of signer-admissible SDVS. By utilizing bilinear pairings and the modified ElGamal signature, we design an efficient identity-based SDVS scheme with signer-admission property. Compared with the existing identity-based SDVS schemes, our scheme supports the signer-admission property, and it is efficient. Copyright © 2013 John Wiley & Sons, Ltd.