This paper presents an improved Mobile WiMAX handover (HO) algorithm for real-time application by using a Link_Going_Down (LGD) trigger technique. Mobile WiMAX is a wireless networking system based on the IEEE 802.16e standard. In order to support phone mobility, a HO scheme of some kind must be adopted, and in this standard hard handover (HHO) is defined as mandatory. Since, the fact that there will be a pause in data transmission during the HO process, delay in communication will occur. Thus, the HO time (>50ms) can degrade system performance when implemented in real-time applications such as Video Streaming or Internet Protocol Television (IPTV). Additionally, the HHO takes approximately 300ms because the HO process doesn't start at the best point. The HHO standard considers only the received signal strength (RSS) to decide initiation. The mobile station velocity is also an important factor in HO initiation that should not be neglected. To deal with the problems of handover delay, this paper proposes a new HO scheme. This scheme adopts the dynamic HO threshold that used LGD technique to define the starting HO process. This technique is based on the RSSD (measured by the Doppler Effect technique), mobile velocities and handover time. Consequently, the HO process starts at the right time and HO time is reduced (<50 ms) and the network resource utilization is enhanced to be more efficient.