Mobile WiMAX aims to provide multimedia multicast/broadcast service (MBS) as well as elastic data service. However, supporting delay sensitive applications like video/audio streaming is still challenging, which requires both efficient handling of link bandwidth and reducing handover delays. To reduce the handover delay in MBS, the IEEE 802.16e standard defines an MBS zone, which is a group of base stations transmitting the same multicast packets. This delay reduction comes at the cost of the high MBS traffic load on Mobile WiMAX networks. In this paper, we propose a location management area (LMA)based MBS handover, dealing with both the bandwidth usage and service disruption. We develop an analytical model to quantify the handover delay and wireless bandwidth usage. Numerical results reveal that the LMA-based handover scheme achieves bandwidth efficient multicast delivery with a slight increase of the average service disruption.