The handover delay time spent in the service connections running at a Mobile Station (MS) in IEEE 802.16e systems can have a negative impact on real-time applications; especially, a connection for Multicast and Broadcast Service (MBS) could suffer additional handover delays due to multicast session update (the process of updating its associated MBS zone), where its MS moves out of its associated MBS zone. Taking this issue into account, this paper proposes an Enhanced Handover Mechanism (EHM) that can create the reduction of both the required time to scan neighbor Base Stations (BSs) and the number of the MBS session update by firstly selecting a neighbor BS guaranteeing a satisfactory level of Received Signal Strength (RSS) value in the current associated MBS zone as the target BS as many as possible. Simulation results show that the EHM can create the reduction of the handover delay time of both multicast and unicast connections while maintaining a satisfactory RSS value of an MS. As a consequence, enhancement of mobility support for real-time MBS can be achieved while keeping compatibility to IEEE 802.16e systems.