The current multi-channel P2P video streaming architectures still suffer from several performance problems such as low Quality of Service (QoS) in unpopular channels. The P2P systems are inherently dynamic, and their performance problems could be categorized into four groups, peer churn, channel churn, uncooperative peers, and geographical distribution of peers. In this paper, for the first time, we develop a novel locality-incentive framework for multi-channel live video streaming. We propose a hierarchical overlay network architecture by utilizing a dual-mode locality-awareness method (spatial and temporal). Moreover, an incentive mechanism for encouraging peers to dedicate their upload bandwidth is introduced. Finally, an efficient buffer-map structure is proposed to predict the validation time of each video chunk request as well as the receiving time of video chunks. We have evaluated the performance of our framework via extensive simulations and compared it with the state-of-the-art method in multi-channel systems. The simulation results demonstrate that the quality of unpopular channels is improved by up to 38%. Moreover, the proposed method improved the quality of video by reducing the playback delay (up to 27%), distortion (up to 39%), and reducing the redundant traffic into the Internet backbones (up to 43%).