A method for supporting session continuity for a terminal in a server. The method according to one embodiment includes sending, by a server, a session continuity operator policy to a first terminal. The session continuity operator policy includes a parameter indicating a preferred network for a transfer of the ongoing session, and session continuity level information including one of a first level and a second level. The method according to the embodiment further includes receiving, by the server, a first session invite message for one of full media transfer and partial media transfer, unless the session continuity level information of the session continuity operator policy is the second level and the first terminal decides not to start the session transfer; and sending, by the server, a second session invite message to the second terminal to achieve session continuity with the first terminal after receiving the first session invite message.