The Long Term Evolution (LTE) network is recognized as the next generation wireless network, which provides high bandwidth and low latency for emerging mobile applications. The issue of power saving is very crucial for the success of service deployment. This paper presents a novel downlink scheduling approach to reduce power consumption while maintaining the receiving quality of video streaming in LTE network. The proposed scheduler considers the buffer length and channel conditions of user equipment (UE) to allocate radio resource, so that the UE can receive as many video packets as possible when the UE is in the RRC-Connected state especially with good channel condition, while the UE will stay in the RRC-Idle state the longer the better to save power given that its buffered video data is enough to play. The 1080P resolution video traffic model was applied for exhaustive simulations to examine the performance of the proposed scheme. The simulation results indicate the tradeoff between the power saving and signaling message overhead issues. And the impacts of related parameters are also studied in this paper.