Methods and an apparatus for providing an edge computing service to a UE in a mobile communication network and. The method comprises: receiving, from an AMF, a PDU session modification command including first information instructing modification of a PUD session for the MEC service and valid time of the PDU session; transmitting, to the AMF, a PDU session modification command NACK message including second information indicating a wait until transmission of an ACK, when relocation of an application context corresponding to the PDU session is possible within the valid time of the PDU session; transmitting, to an MEC system providing the service, an application context relocation request message; and transmitting, to the AMF, a PDU session modification command ACK in response to receiving an application context relocation complete message from the MEC system, wherein the PDU session modification command and the PDU session modification command NACK message are NAS messages.