A technique for managing a packet to be transmitted to a Mobile Station (MS) that performs Relay Station (RS) handover in a multi-hop relay Broadband Wireless Access (BWA) system is provided. In the BWA system, a Base Station (BS) includes a controller for determining whether to perform activecasting on an MS upon receiving an activecast request message; a scheduler for allocating a resource by taking into consideration a channel condition between the MS and a serving RS when activecasting is determined to be performed; and a transmitter for multicasting a packet, which is to be transmitted to the MS, to a target RS and the serving RS by using the allocated resource.