Method and apparatus for a user equipment (UE) performing random access are disclosed. For this end, the UE transmits first multiple random access preambles for a random access procedure to the network, and monitors random access responses respectively corresponding to each of the first multiple random access preambles during each of multiple random access response reception windows. The UE transmits second multiple random access preambles for the random access procedure to the network, if a random access response reception of the first multiple random access preambles is determined as not successful. Here, the random access response reception is determined as not successful, when none of the random access responses is successfully received until a last random access response reception window among the multiple random access response reception windows ends.