The present document relates to a method in which user equipment carries out a process for random access to a base station in a carrier aggregation mobile communication system which performs communications using a plurality of component carriers (CCs), and to a terminal device for the method. The user equipment separately manages back-off operations for each of the CCs, and performs a random access preamble transmission using the relevant CC if another usable CC exists, even when a back-off period is being applied to a specific CC, to carry out a random access process in an efficient manner in a carrier aggregation mobile communication system.