The present invention relates to a method and an apparatus for supporting a handover and, more particularly, to a method and an apparatus for changing a mobile management entity while maintaining a connection state of a connection mode terminal. In order to achieve the above-mentioned objective, a method for supporting a handover of a serving mobile management entity (MME) according to one embodiment of the present invention comprises the steps of: receiving a tracking area update (TAU) request message from a terminal: determining whether the serving MME of the terminal needs to be changed, on the basis of the TAU request message; and transmitting, in the case where it is determined that the serving MME of the terminal needs to be changed, an MME change request message to an eNB.