A method and apparatus for controlling discontinuous transmission and reception are disclosed. A Node-B schedules an offset for discontinuous transmission (DTX) and/or discontinuous reception (DRX) for a user equipment (UE) and sends the offset to the UE. The UE then shifts the DTX and/or DRX pattern based on the received offset. The UE may modify the offset based on the transmission time of an activation command for DTX and DRX. The UE may modify an offset for DTX and DRX to shift the DTX pattern and DRX pattern when the UE receives downlink data or transmits uplink data based on a sub-frame number at the time of the downlink reception and uplink transmission.