There has been a recent rapid growth of interest in efficient cryptographic protocols that carry proofs in the standard model. Avoiding the random oracle model is to be preferred, given the known problems with instantiating these models in practice. However, among the existing authenticated key agreement protocols, some protocols were based on the identity based encryption schemes which are not prove secure, so the protocols can not be guarantee security; the others have been proven secure just hold in relatively weak models which do not fully support the session-state reveal or ephemeral-key reveal query, that lead to poor secure protocols. In this paper the idea of the MTI protocols is adopt to devise a new identity based authenticated key agreement protocol for two-party in standard model, which based on the truncated decisional augmented bilinear Diffie-Hellman exponent and decisional bilinear Diffie-Hellman assumptions. The formal proof is provided to show that the proposed scheme is provably secure in the enhanced Canetti-Krawczyk (eCK) model, which better supports the adversarys queries. To our best of our knowledge, the scheme is the first identity based authenticated key agreement in the eCK model and standard model. Moreover the proposed protocol has more performances in computational and communication efficiencies compared with all known protocols in standard model.