With advent of various mobile devices with powerful networking and computing capabilities, the users' demand to enjoy live video streaming services such as IPTV with mobile devices has been increasing rapidly. However, it is challenging to get over the degradation of service quality due to data loss caused by the handover. Although many handover schemes were proposed at protocol layers below the application layer, they inherently suffer from data loss while the network is being disconnected during the handover. We therefore propose an efficient application-layer handover scheme to support seamless mobility for P2P live streaming. By simulation experiments, we show that the P2P live streaming system with our proposed handover scheme can improve the playback continuity significantly compared to that without our scheme.