Mobile users frequently suffer from long buffering time and intermittent breaks of video streaming, due to the instability of mobile wireless link caused by signal fluctuation and user's mobility. Although the scalable video coding techniques are adopted recently, it brings a huge encoding overhead to video providers, and induces a large amount of bandwidth waste. In this paper, we propose a new video streaming framework for mobile users, called AMVP-Cloud, which is composed of two core parts: the Adaptive Mobile Video Streaming (AMoS), and the User Behavior Oriented Video Pre-Fetching (UBoP). AMVP-Cloud efficiently stores and transfers videos in clouds, and constructs a private agent for each mobile user to provide "non-terminating" streaming experience, which can adapt to the fluctuation of link quality based on the scalable video coding and feedback from mobile side. Also referring to the user model for video watching, AMVP-Cloud can try to provide "non-waiting" streaming experience by background pre-fetching among the video agents and local storage of mobile side. Finally, we evaluate our prototype implementation and verify that AMVP-Cloud can offer good adaptability and short streaming delay as well as pre-fetching delay.