The present invention relates to a transmission of a random access in a specific cell from a plurality of serving cells in a mobile communication system using a carrier aggregation technology, and a method for efficiently transmitting uplink channels other than the random access in another cell. In particular, the method for a terminal to transmit an uplink channel to a base station comprises the steps of: confirming whether an uplink channel for a second carrier having an uplink timing different from a first carrier is included in a subframe transmitting a Random Access Preamble for the first carrier; if included, confirming whether the sum of the electric power required for the transmission of the random access preamble and the electric power required for the transmission of the uplink channel exceeds the maximum transmission electric power of the terminal; and, if exceeding, transmitting the random access preamble preferentially before the uplink channel. In addition, the terminal for transmitting an uplink channel to a base station comprises: a transmitter/receiver for transmitting/receiving a signal to/from the base station; and a control unit for confirming whether the uplink channel for a second carrier having an uplink timing different from a first carrier is included in a subframe for transmitting a random access preamble for the first carrier, and if included, confirming whether the sum of the electric power required for transmitting the Random Access Preamble and the electric power required for transmitting the uplink channel exceeds the maximum transmission electric power of the terminal, and if exceeding, controlling the transmission so that the random access preamble is preferentially transmitted before the uplink channel.