The Internet research community has proposed many routing protocols to support efficient multicast application. However, these protocols were developed for multicast parties whose members are topologically stationary, and they thus do not support both mobile receivers and mobile sources. Unfortunately, the mobility of the multicast source is a challenging problem to solve. When a multicast source moves from one IP network to another, it obtains a new IP address. However, since IP multicast is receiver-initiated, and the multicast delivery tree is constructed based on the multicast source?s address, the multicast traffic cannot be delivered to multicast receiver unless a new delivery tree is built. As a consequence, the multicast routing entities require new multicast routing states and multicast receivers need to be notified whenever the handover occurs. This induces a non-transparent mobility, and leads to session disruption. To overcome these drawbacks, this paper presents a new solution to make multicast source mobility transparent to both multicast receivers and on-tree multicast routers. This solution, called Mobility-aware Rendezvous Point, extends the PIM-SM Rendezvous Point with mobility awareness, and introduces new techniques for the source registration with the Rendezvous Point. Simulation results have proved that the solution avoids the reconstruction of a multicast tree after the handover of the multicast sources.