Provided is a method and apparatus for transmitting sidelink data by a first user equipment (UE) in a wireless communication system supporting sidelink communication between the first UE and a second UE. The method includes identifying configuration information including information associated with discontinuous reception (DRX) for the sidelink communication, and in case that the second UE performs a DRX operation, transmitting the sidelink data to the second UE in a DRX active time, the DRX active time of the second UE being identified based on the configuration information.