A method of supporting group communication over LTE MBMS is provided. A UE first establishes a unicast Evolved Packet Service (EPS) bearer in an LTE network for group communication. The UE belongs to a communication group having a communication group ID. The UE receives access information from the network for monitoring downlink (DL) multicast traffic of the DL group communication based on a multicast decision. The UE is then ready for monitoring a multicast Multimedia Broadcast Multicast Service (MBMS) bearer for receiving the DL multicast traffic. In one embodiment, The UE requests to switch the DL multicast traffic from the multicast MBMS bearer to the unicast EPS bearer upon detecting that the UE is approaching an MBMS coverage boundary. In another embodiment, the UE transmits an indication of preferred target cells to the network before performing a handover and thereby maintaining multicast service continuity of the group communication.