An apparatus and a method for supporting multicast communication in a broadband wireless access system are provided. A method of a Mobile Station (MS) for supporting multicast communication in a wireless access system includes acquiring decoding parameters by receiving an Advanced Air Interface Enhanced-Multicast and Broadcast Service configuration (AAI-E-MBS_CFG) message from a Base Station (BS), establishing an E-MBS service flow by sending and receiving AAI Dynamic Service Addition-request/response (AAI_DSA-REQ/RSP) messages to and from the BS, and decoding E-MBS MAP received from the BS through the established E-MBS service flow using the acquired decoding parameters. The E-MBS MAP includes information for decoding multicast bursts.