Mobile opportunistic network (MON) is an efficient way of communication when there is no persistent connection between nodes. Multicast in MONs can be used to efficiently deliver messages to multiple destination nodes. However, because multiple destination nodes are involved, multicast routing is more complex than unicast and brings a higher communication cost. Backbone-based routing can effectively reduce the network overhead and the complexity of routing scheme. However, the load of backbone nodes is larger than that of regular nodes. If the backbone node’s buffer is exhausted, it will have a significant impact on the performance of the routing scheme. Load balancing can improve the ability of backbone to deal with the change of network load, and backbone maintenance algorithm can provide backbone robustness. In this paper, we propose a robust load-balanced backbone-based multicast routing scheme in MONs. In the backbone construction algorithm, we transform the problem of backbone construction into a multi-objective optimization problem, and propose a multi-objective evolutionary algorithm-based backbone construction algorithm, namely LBMBC-MOEA algorithm. In addition, in order to increase the robustness of the backbone-based routing scheme, we propose a localized multicast backbone maintenance algorithm (MBMA) to deal with the buffer exhaustion of backbone nodes. When a backbone node’s residual buffer is insufficient, MBMA algorithm selects other nodes to replace the backbone node. The results on extensive simulations show that when considering the node buffer size constraints, compared with previous backbone-based multicast routing schemes, our proposed algorithm has better performance, and when the node’s residual buffer is insufficient, MBMA algorithm can significantly improve the performance of the backbone-based multicast routing scheme.