In recent years, Mobile Network has evolved greatly with the existences of MANET, Wireless Sensor Network, Mobile IP, NEMO and etc. The advent of Network Mobility (NEMO) tends to provide seamless Internet Connectivity to all the nodes within a Mobile Network regardless of their current points of attachment with the usage of a Mobile Router. Multicasting support is one of the key technologies in next generation network as well as in network mobility environment especially for multicast based group-oriented services. However, multicasting support remains to be a challenging problem in NEMO as the entire network with multicast service moves away. In addition, a nested NEMO environment prohibits the multicasting service from the Parent-NEMO to the Sub-NEMO to be supported completely. Thus, we propose and explain a proper solution with the adaption of a well known multicast routing protocol, On-Demand Multicasting Routing Protocol (ODMRP) to fully support multicasting in NEMO.