To date, some identity based strong designated verifier signature schemes have been proposed, but there are some drawbacks on these schemes. To overcome the problem above, in this paper, a novel identity based strong designated verifier signature scheme is proposed from bilinear map. The proposed scheme is secure in the random oracle model under the bilinear Diffie-Hellman assumption. From the performance comparison with the existing schemes, it can be concluded that the proposed scheme has lower computational cost and shorter size of signature.