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Designated verifier signature scheme (DVS) is an impor- tant cryptographic primitive which can provide authentica- tion of a message without a non-repudiation property of tra- ditional signature. The security of most existing schemes is only proven in the random orale model. However, the se- curity in random oracle model doesn't imply the security in the real world. In this paper, we proposed an efficient Designated verifier signature scheme without random ora- cle and show that the security of the scheme is tightly re- lated to Strong Diffie-Hellman assumption. The prominent advantage of the scheme is that the pairing operation is not involved in signing phase, thus the scheme is very suitable for the device which has low computation.