In a cellar system providing various packet services, sleep mode operation of a terminal in an idle state is controlled. The cellular system determines a discontinuous receiving (DRX) period according to a QoS of a packet service provided to the terminal, and runs the sleep mode according to the determined DRX period. The cellular system runs the sleep mode divided into shallow sleep duration and deep sleep duration. With this manner, a paging delay to the terminal and a power consumption of the terminal may be reduced.