A method, performed by a first Session Management Function (SMF), for providing a continuous service to a user equipment (UE) includes: identifying, by the first SMF, triggering of an SMF change operation; transmitting, to an Access and Mobility Management Function (AMF), a message indicating a change in a status of a Packet Data Unit (PDU) session of the UE so as to request a procedure of changing an SMF; receiving a context request message requesting a context of the UE from a second SMF that is a target SMF; and transmitting a context request response message to the second SMF.