Mobile IP (MIP) is the solution supporting the mobility of Mobile Nodes (MNs), however, it is known to lack the support for NEtwork MObility (NEMO). NEMO manages situations when an entire network, composed of one or more subnets, dynamically changes its point of attachment to the Internet. NEMO Basic Support (NBS) protocol ensures session continuity for all the nodes in a mobile network, however, there exists a serious pinball routing problem. To overcome this weakness, there are many Route Optimization (RO) solutions such as Bi-directional Tunneling (BT) mechanism, Aggregation and Surrogate (A&S) mechanism, Recursive Approach, etc. The A&S RO mechanism is known to outperform the other RO mechanisms, except for the Binding Update (BU) cost. Although Improved Prefix Delegation (IPD) reduces the cost problem of Prefix Delegation (PD), a well-known A&S protocol, the BU cost problem still presents, especially when a large number of Mobile Routers (MRs) and MNs exist in the environment such as train, bus, ship, or aircraft. In this paper, a solution to reduce the cost of delivering the BU messages is proposed using a multicast mechanism instead of unicasting such as the traditional BU of the RO. The performance of the proposed multicast-based BU scheme is examined with an analytical model which shows that the BU cost enhancement is up to 32.9% over IPDbased, hence, it is feasible to predict that the proposed scheme could benefit in other NEMO RO protocols.