Provided are a method for performing a handover by a user equipment (UE) in a wireless communication system, and an apparatus supporting the same. The method may include: receiving information on candidate target cells for the handover and a handover condition, from a base station; initiating a handover to a first target cell among the candidate target cells, based on the handover condition; before detecting a failure of the handover to the first target cell, when channel quality of a second target cell among the candidate target cells is higher than channel quality of the first target cell, stopping the handover to the first target cell; and performing a handover to the second target cell.