The efficiency of live Peer-to-Peer (P2P) streaming protocols depends on the appropriateness and the management abilities of their underlying overlay multicast. While a tree overlay structure confines transmission delays efficiently by maintaining deterministic delivery paths, an overlay mesh structure provides adequate resiliency to peers dynamics and easy maintenance. On the other hand, content freshness, playback fluidity and streaming continuity are still challenging issues that require viable solutions. In this paper, we propose a Hybrid Live P2P Streaming Protocol (HLPSP) based on a hybrid overlay multicast that integrates the efficiency of both the tree and mesh structures. Extensive simulations using OMNET++ are conducted to investigate the efficiency of HLPSP in terms of relevant performance metrics, and position HLPSP with respect to DenaCast the enhanced version of the well-known CoolStreaming protocol. Simulation results show that HLPSP outperforms DenaCast in terms of startup delay, end-to-end delay, play-back delay and data loss.