A random access method and an apparatus of a terminal for performing random access procedure to multiple base stations in parallel in a Long Term Evolution (LTE) system supporting dual connectivity are provided. The method includes determining whether a first preamble transmission to a first cell of a first base station is overlapped with a second preamble transmission to a second cell of a second base station in a time domain, determining, when the first preamble transmission is overlapped with the second preamble transmission in the time domain, whether a sum of transmit powers calculated for the first and second preamble transmissions is greater than a maximum allowed transmit power of the terminal, and controlling, when the sum of the first and second preamble transmit powers is greater than the maximum allowed transmit power, the transmit power calculated for the second preamble transmission.