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Mobile WiMAX based on IEEE802.16e standard supports various kinds of broadband data services such as VOD, VoIP, and MBS (multicast broadcast service). Unlike wired networks, however, wireless networks have limited bandwidth. MBS overcomes this problem using a shared downlink channel for efficiently supporting a number of users. However, its coverage and throughput are significantly affected by the operational condition. In this paper we propose to employ mobile multi-hop relay (MMR) along with an adaptive modulation and coding (AMC) scheme to increase the performance of MBS. The result of computer simulation with NS-2 shows that the throughput and transmission time are substantially improved by using the proposed approach compared to the existing MBS system.