A method and an apparatus for allowing a mobile terminal in a connected state to perform a DRX(Discontinuous Reception) operation in a mobile communication system are provided to allow a mobile terminal to report a channel situation after checking whether actual data is transmitted and to prevent the terminal from reporting periodically the channel situation unnecessarily. A DRX controller(1035) receives forward data for controlling ON/OFF of power supply of a receiving unit by using DRX period information, DRX initial start point information, time information for reporting a channel state, and time information for receiving a transmission resource allocation message. A control channel processing unit(1020) controls the receiving unit to be turned on at a wake-up timing, receives a control channel, and checks an indicator indicating whether the forward data is to be transmitted. A reverse synchronization control unit(1025) performs uplink synchronization according to the result of the control channel processing unit(1020). A channel state reporting unit(1030) reports the channel state after the time information for reporting the channel state. A transmitting/receiving unit(1040) receives the forward data after the time information for receiving a transmission resource allocation message.