A method for random access to a base station by a user equipment (UE) in a mobile communication system using carrier aggregation in which communication is conducted over a plurality of component carriers, and a terminal for the method are disclosed. When the UE performs a contention-based random access procedure in the mobile communication system to which CA technology is applied, the UE considers an uplink grant signal as a contention resolution message when receiving the uplink grant signal from a eNB only when the uplink grant signal is received through a downlink CC corresponding to an uplink CC used to transmit a random access preamble or a third message, to thereby prevent contention resolution from being erroneously ended.