An efficient and practical authenticated key agreement protocol based on the line of geometry is proposed in this paper. It is a good solution to provide authentication and confidentiality. Identity authentication and message confidentiality are two important issues for the open network environment. In the proposed protocol, the authorized user can access multi-servers securely by keeping only a weak password and a smart card. Owing to the limited memory of the smart card, the secret information stored in the smart card has a size independent of the number of servers to which it connects. The proposed protocol provides mutual authentication between the user and the server and enables them to establish a common session key to provide message confidentiality for each other. It can also resist the replay attack, the impersonation attack, the off-line dictionary attack, the known key attack, the unknown key share attack, the stolen verifier attack and the insider attack. The security of the proposed protocol will be demonstrated by the random oracle model. Furthermore, we use the logic analysis method to analyze the proposed protocol. This protocol does not use any overload cryptographic operations and requires less communicational and computational costs than the results obtained previously from the existing scholarship.