A session mobility support is disclosed. An application server (AS) can accurately recognize a session update by checking a Replace header, a user ID and a media element included in a session invitation message (or an SIP-based INVITE message) received from a UE (User Equipment), to thus guarantee successful mobility of a session. In addition, in order to allow the AS to accurately recognize the session update, the UE first transmits the session invitation message including the Replace header via a PS (Packet Switching domain, and then, after a response to the session invitation message is received, the UE transmits a call setup message (e.g., SETUP message) via a CS (Circuit Switching) domain.