A communication method and device in a wireless communication system supporting edge computing is provided. A method of a UE including an EEC in a communication system supporting an edge computing service using an EDN exchanging application data traffic with the UE is provided, the method comprises identifying whether the UE supports a SMS over NAS, transmitting, to an ECS managing configuration information of the EDN, a first service provisioning request message including an indication of the SMS over the NAS supported in case that the UE supports the SMS over the NAS, and in case that the UE receives, through a network from the ECS, an SMS message including triggering information related to an update of the configuration information, transmitting, to the ECS, a second service provisioning request message based on the triggering information.