In this paper, we propose QoS-constrained peer selection and nondisruptive rate adaptation schemes with considering shared bottleneck problem to provide a stable peer-to-peer live video streaming service during vertical handoff. In the proposed scheme, a QoS-constrained peer is selected by estimating bandwidth with active probing, and a reception rate converges to a stable state without any QoS degradation with help of multi-path handoff. The shared bottleneck problem is addressed by adjusting the estimated bandwidth and yielding the redundant bandwidth usage.