A method, medium, and apparatus controlling a handover between different network types, including the operations of transmitting a message requesting a transmission bandwidth change, so as to have a transmission bandwidth supported by a new network after movement of the mobile terminal, from the mobile terminal to the server after performing the handover, changing the transmission bandwidth of the server to be supported by the new network based on the transmitted message of requesting the bandwidth change, transmitting a message acknowledging the changed transmission bandwidth from the server to the router, and transceiving data through a new data transmission tunnel between the router and a new access point within the new based on the message acknowledging the changed transmission bandwidth. Accordingly, loss of data packets occurring when a handover is performed may be effectively prevented.