A method and apparatus for performing a L3handover between CNs in a packet-switched network are provided. When a UE moves from an old RAN to a new RAN, the UE sends a measurement report message including cell information to the old RAN. The old or new RAN determines whether to perform a L3 handover. If the L3 handover is required, a tunnel is established between the new RAN and a new CN. The UE performs a handover from the old RAN to the new RAN, without establishing a tunnel between the new RAN and an old CN. Upon detection of the movement of the UE, the new RAN sends a L2 handover complete message to the old RAN. After moving to the new RAN, the UE acquires a new IP address, performs the L3 handover, and communicates with the new CN through the new RAN.