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Cryptographic hash function plays a central role in application of cryptology and is an essential building block of a digital signature scheme. So far, in almost all of the practical digital signature schemes, hash functions which are dependent on underlying cyclic groups are necessary, and it could be required to construct a dedicated hash function for each digital signature. As a special cryptographical tool, designated verifier signature scheme (DVS) is a signature scheme which provides authentication of a message without providing a non-repudiation property of traditional signature. Thus, designated verifier signature scheme plays an important role in copyright protection. However, most of existing schemes include hash functions as a random generator to realize security proof, thus it results in the security of most existing schemes is only proven in the random oracle model. However, security 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 hash function and show that the security of the scheme is tightly related to weak inverse of computational Diffie-Hellman assumption. The prominent advantage of the scheme is that the pairing operation and hash function are not involved in signing phase, the size of signature is 480 bits. Thus the scheme is very efficient.