A method and apparatus for a user equipment (UE) performing a random access to a network are disclosed. For this end, the UE selects a first carrier for the random access among multiple carriers, and transmits a first random access preamble for a first random access procedure via the first carrier to the network. Then, the UE applies backoff time to the first carrier and reselects a second carrier for the first random access procedure among the multiple carriers, when the first random access procedure is determined as not successful; and transmits a second random access preamble via the second carrier to the network. Here, reselecting the second carrier is performed before the backoff time applied to the first carrier ends.