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This paper presents the design and evaluation of a highly efficient on-demand multicast routing protocol for mobile ad hoc networks (MANETs). The protocol, called Geography-aided Multicast Zone Routing Protocol (GMZRP), eliminates as much as possible duplicate route queries by using a simple yet effective strategy for propagating the multicast route request (MRREQ) packets. GMZRP is the first hybrid multicast protocol taking the advantages of both topological routing and geographical routing. It partitions the network coverage area into small zones and guarantees that each geographic zone is queried only once. GMZRP maintains a multicast forwarding tree at two levels of granularities, i.e., the zone granularity and the node granularity. By doing this, it can easily handle route breakage since the zone level information can help recover the link failure at the node level. The results of the performance evaluation of GMZRP using simulation show that, comparing with the well-known multicast protocol ODMRP (On-Demand Multicast Routing Protocol), GMZRP has much lower protocol overhead in terms of query packets and, meanwhile, achieves competing packet delivery ratio and shorter delivery latency.