Abstract: In order to protect the privacy of the signature receiver in applications,directed signature schemes have the property that the signature can be verified only with the help of the signature receiver of the signer.A directed signature scheme based on identity with fairness is proposed by bilinear maps on elliptic curve cryptosystem based on identity.When the signer and the verifier disputes,trusted third party can check the signature validity with the help of the signer or the designated verifier as well.It is shown our scheme is more efficient and shorter in size than the existing directed signature schemes.