The present invention discloses a variety of methods of supporting handover in a wireless access system. A handover support method according to an embodiment of the present invention includes the steps of: transmitting a handover request message to a first base station (serving base station); receiving a handover response message (UL grant or UL-MAP message) containing authentication information (M) from a second base station (target base station); deriving a dedicated code index (DCI) for instructing a dedicated ranging code by using the authentication information (M); transmitting the dedicated ranging code to the second base station on a non-contention basis; and receiving a ranging response message as a response for the dedicated ranging code.