To provide the mobility for mobile stations, handover is a critical issue to be assessed. Many studies about handover addressed the various fast handover schemes for seamless handover. However, shortening the handover latency is not the only and the best cure to apply to all kinds of applications, especially for store-forward video streams and non-interactive live video streams. In this paper, a seamless service handover concept and a mechanism are proposed. The proposed solution approaches the actually best solution to the seamless service for transporting the store-forward and non-interactive live Scalable Video Coding streams over the IEEE 802.16e mobile WiMAX network. The simulation results show that the seamless service strategy and mechanism indeed improve the continuity of the SVC video streaming service when the mobile station moving between two mobile WiMAX base stations and suffering the inevitable handover.