The Session Initiation Protocol (SIP) is a signaling communications protocol, which has been chosen for controlling multimedia communication in 3G mobile networks. In recent years, password-based authenticated key exchange protocols are designed to provide strong authentication for SIP. In this paper, we address this problem in two-party setting where the user and server try to authenticate each other, and establish a session key using a shared password. We aim to propose a secure and anonymous authenticated key exchange protocol, which can achieve security and privacy goal without increasing computation and communication overhead. Through the analysis, we show that the proposed protocol is secure, and has computational and computational overheads comparable to related authentication protocols for SIP using elliptic curve cryptography. The proposed protocol is also provably secure in the random oracle model.