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In this paper, we propose a new heuristic algorithm called Multicast Multi-domain Dedicated Protection (MMDP) to provide survivability in multicast multi-domain optical networks. In route computation, MMDP considers the load balancing. To provide the intra-domain protection, MMDP uses the modified Minimal-cost Path Heuristic (MPH) algorithm to compute the intra-domain survivable multicast tree. To provide the inter-domain protection, based on multi-domain logical topology, MMDP firstly uses MPH algorithm to compute the inter-domain logical multicast tree and then uses Dijkstra algorithm to compute the inter-domain logical backup sub-path for each inter-link on this logical multicast tree. Simulation results show that MMDP has better performances than traditional algorithm.