Unlike Video on Demand (VoD) which is able to pause at any time, live streaming multimedia must play a video without interruption. This research focuses on the transmission of live streaming multimedia and develops a Continuing Service System (CSS) in the IP router, generally used in the family, to complete the "Time-Shifting" and "Streaming Hand-Off" mechanism. The purpose of this research breaks the limitations of time and space in the streaming transmission and provides users with a continuing service of viewing all live streaming multimedia programs no matter whether they leave temporally or have to change the watching location.