The present invention relates to a method for performing a random access procedure by a user equipment in a wireless communication system. In particular, the method includes transmitting a first number of random access preambles; detecting a second number of random access responses corresponding to the first number of random access preambles; and transmitting an payload using one uplink grant for which a listen before talk (LBT) procedure is firstly successful among a second number of uplink grants included in the second number of random access responses.