A method and apparatus for supporting a handover through the Internet. A source proxy performs receiving, through an eNB from a UE, a connection request to a server, establishing a first TCP session with an anchor proxy designated for the server, and transferring data received from the server through the first TCP session, receiving a handover preparation notification including an IP address of the UE from the eNB, as the UE is handed over to a target eNB; transferring session information associated with the first TCP session and information associated with a target proxy related with the target base station; transferring, to the target proxy, the session information associated with the first TCP session, and when a handover start notification is received from the eNB, freezing the first TCP session, and transferring, to the target proxy, state information associated with data being transmitted through the first TCP session.