Strong designated verifier signature scheme enables the designated receiver to identify the source of a received message and prevent a third party from identifying the source of the message, which is well suitable for E-commerce and E-government applications. Based on decisional bilinear Diffie-Hellman assumption and gap bilinear Diffie-Hellman assumption, using bilinear pairing, a new strong designated verifier signature scheme is proposed. The security of the scheme is proved under standard model. The analytical results show that the new proposed protocol has unforgeability, non-transferability, privacy of the signer’s identity and non-delegatability for signature verification. This scheme is based on bilinear pairing, which means that it needs no certificate and has a simple key management. On the other hand, it is efficient in communications and computation, and implementation is simple, so that it could be implemented in mobile devices with low power and small processor.