Dynamic adaptive bitrate (ABR) streaming has recently been widely deployed in wireless networks. It, however, does not impose adaptation logic for selecting the quality of video chunks for mobile users. In this paper, we propose a two time-scale resource optimization scheme for ABR streaming over wireless networks under time-varying channels. Our proposed resource optimization scheme takes into account three key factors that make a critical impact on quality of experience (QoE) of ABR streaming, including video quality, quality variation, and video rebuffer. Lyapunov optimization technique is employed to maximize the QoE of users by dynamically adapting the video quality at the application layer and allocating bandwidth at the physical layer. Without the prior knowledge of channel statistics, we develop a video streaming algorithm (VSA) to obtain the video quality adaptation and bandwidth allocation decisions. For the arbitrary sample path of channel states, we compare the QoE achieved by VSA with that achieved by an optimal T-slot lookahead algorithm, i.e., knowledge of the future channel path over an interval of length T time slots. Simulation results demonstrate the effectiveness of the proposed VSA for ABR streaming over time-varying wireless networks.