In a multi-source video streaming system, premature draining of low-power nodes can cause sudden failures of peer connections and degrade streaming performance. To solve this problem, we propose an energy-aware scheduling (EAS) scheme to better distribute the streaming load among different peers by jointly considering network conditions and node energy levels. We model the proposed scheme using a rate/energy-distortion optimization framework and heuristically solve it using the concept of asynchronous clocks. Simulation studies show that the proposed EAS scheme can achieve comparable streaming quality while consuming less energy.