A method and device are disclosed for a User Equipment (UE) to sidelink discontinuous reception (DRX) for sidelink groupcast communication associated with a group. In one embodiment, the method includes the UE assuming or considering a sidelink DRX configuration applied for the sidelink groupcast communication associated with the group, wherein the sidelink DRX configuration comprises at least one of an on-duration timer length used for determining an on-duration at the beginning of each sidelink DRX cycle and/or a cycle length used for determining a length of each sidelink DRX cycle. The method also includes the UE deriving or determining a time to start of on-duration for each sidelink DRX cycle or start of each sidelink DRX cycle based on at least an identifier associated with the group. The method further includes the UE transmitting a sidelink control information associated with the group on a sidelink control channel in a period, wherein the period is determined based on the SL DRX configuration and the time to start of on-duration for each sidelink DRX cycle or start of each sidelink DRX cycle.