A server, terminal, and method for supporting mobility in a network are provided. A server includes a storage which stores a double chord lookup table including server search information based on identifiers and location information of terminals on a network, a controller which finds a server for providing an optimal routing path between a receiving terminal and a transmitting terminal for sending a packet to the receiving terminal, using the double chord lookup table, where a trigger including an identifier and location information for identifying the receiving terminal is received from the receiving terminal, and a communicator which reports the location of the found server to the receiving terminal and the transmitting terminal.