A method for continuously providing an edge computing service to user equipment (UE) by an edge enabler server (EES) of a mobile edge computing (MEC) system is provided, which includes receiving, from a source edge application server (EAS), update information including UE information and source EAS information, wherein the source EAS provides the edge computing service to the UE; retrieving, from an edge configuration server (ECS), target EES information based on the update information; transmitting, to a target EES, the UE information and the EAS information based on the target EES information; receiving, from the target EES, target EAS information; and transferring, to the source EAS, the target EAS information.