Concerning the flaw that it needs a fully credible third party in ID-based strong designated verifier signature and the low efficiency of existing schemes,taking the advantage of Certificate Authority(CA)'s low trust level in certificate-based public key cryptography,a new strong designated verifier signature scheme was proposed in this paper.Furthermore,the formal security analysis under assumed Bilinear Diffie-Hellman(BDH) problem in the random oracle model was presented.Performance analysis shows the scheme meets all properties of strong designated verifier signature schemes and enjoys higher correspondence efficiency used in bandwidth limited environment since the signature length is just one of the group elements.