The session initiation protocol (SIP) is a challenge-response based authentication protocol which is used in 3G mobile networks. In 2010, Chen et al. proposed an authentication protocol for SIP using elliptic curves cryptography. However, this paper show that the Chen et al. authentication scheme is vulnerable to off-line password guessing attack, and does not provide perfect forward secrecy. To overcome their weaknesses, a security-enhanced authentication scheme for SIP is proposed, which not only defends against the off-line password guessing attack, but also supports perfect forward secrecy.