This paper proposes an ID-based entity-aunthentication and authenticated key exchange protocol with ECC via two-pass communications between two parties who airs registered to the trusted third-party KC in advance. The proposed protocol developed by applying ECDSA and Diffie-Hellman key exchange scheme to the ID-based key distribution scheme over ECC proposed by H. Sakazaki, E. Okamoto and M. Mambo(SOM scheme). The security of this protocol is based on the Elliptic Curve Discrete Logarithm Problem(ECDLP) and the Elliptic Curve Diffie-Hellman Problem(ECDHP). It is strong against unknown key share attack and it provides the perfect forward secrecy, which makes up for the weakness in SOM scheme,