The present invention relates to a wireless communication system which supports carrier aggregation. More particularly, the present invention relates to a method and to an apparatus for enabling a user equipment to perform a handover in a wireless communication system which supports carrier aggregation. The method for performing a handover comprises the steps of: transmitting a measurement report on a target cell to a serving cell; receiving, from the serving cell, a message containing a signature route sequence index, cyclic shift parameters, and information related to the component carrier of the target cell; confirming contention-based signatures generated on the basis of the signature route sequence index and cyclic shift parameters; and transmitting one of said contention-based signatures to the target cell for random access, via one or more component carriers, on the basis of said information related to the component carrier. The present invention also relates to an apparatus for the method.