The video streaming technique and 4G LTE networks have been developing at a high speed, while the advancement of the battery technology is relatively slow. A lot of efforts have been made on understanding the power consumption in general 4G LTE networks, while little attention has been focused on reducing the power consumption of mobile devices for online video streaming in 4G LTE networks. In this paper, we attempt to develop efficient optimization techniques to address this problem. It is an important and also interesting problem, while there are many challenges needing to be alleviated (e.g., the uncertainty of users' behavior modes). To attack the challenges, we suggest a self-adaptive method that can allow us to adjust various parameters dynamically and efficiently, achieving a relatively small energy consumption. We give the rigorous theoretical analysis for the proposed method, and conduct the empirical study to validate its effectiveness.