Recently, Lu et al. and Chaudhry et al. presented an authenticated key agreement scheme for session initiation protocol (SIP), respectively. They illustrated their schemes are secure against various familiar attacks. However, we demonstrate Lu et al.’s scheme is vulnerable to stolen verifier attack and Chaudhry et al.’s scheme is insecure to session key attack. To solve these problems, we propose a new provably secure mutual authentication scheme for SIP. Informal security analysis illustrates this proposed protocol can withstand different kinds of familiar attacks including stolen verifier attack and session key attack. And the correctness and security of the proposed protocol is also proved through Protocol Composition Logic (PCL) and generic group model. Eventually, security comparison shows our proposed scheme is more secure and performance analysis demonstrates the computation cost is also acceptable.