We propose a methodology to design user-aware streaming strategies for energy efficient smartphone video playback applications (e.g. YouTube). Our goal is to manage the streaming process to minimize the sleep and wake penalty of cellular module and at the same time avoid the energy waste from excessive downloading. The problem is modeled as a stochastic inventory system, where the real length of video playback requested by the smartphone user is considered as demand that follows a stochastic process. Through user behavior analysis, a Gaussian Mixture Model (GMM) is constructed to predict the user demand in video playback, and then an energy efficient video downloading strategy will be determined progressively during the playback process. Experimental results show that compared to a static downloading strategy that is optimized by exhaustive trail, our method can reduce the wasted energy by 10 percent in average.