Authentication schemes have been widely deployed access control and mobility management in various communication networks. Especially, the schemes that are based on multifactor authentication such as on password and smart card come to be more practical. One of the standard authentication schemes that have been widely used for secure communication over the Internet is session initiation protocol (SIP). The original authentication scheme proposed for SIP was vulnerable to some crucial security weaknesses. To overcome the security problems, various improved authentication schemes have been developed, especially based on elliptic curve cryptography (ECC). Very recently, Zhang et al. proposed an improved authentication scheme for SIP based on ECC using smart cards to overcome the security flaws of the related protocols. Zhang et al. claimed that their protocol is secure against all known security attacks. However, this paper indicates that Zhang et al. protocol is still insecure against impersonation attack. We show that an active attacker can easily masquerade as a legal server to fool users. As a remedy, we also improve Zhang et al. protocol by imposing a little extra computation cost.