The shortage of security in the authentication and key agreement protocol for the mobile communication system are proposed,an key agreement and mutual authentication scheme based on elliptic curve cryptograph techniques is proposed.The mutual authentication and agreement on a secure session key is realized,between users,or between user and network server in the mobile network.By using the ECC techniques,greater security with fewer bits is provided.As the result,the bandwidth requirement is less,and furthermore,computational burden and storage requirement is also lower on the mobile terminals.