While the demands of video streaming services over the mobile networks have been souring over these years, the wireless link capacity cannot practically keep up with the growing traffic load. The gap between the traffic demand and the link capacity, along with time-varying link conditions, results in poor service quality of video streaming services over the mobile networks, such as intermittent disruptions and long buffering delays. Leveraging the current cloud computing technology, we propose and discuss a framework to improve the quality of video services for mobile users, which includes two parts: cloud-assisted adaptive video streaming, and social-aware video prefetching. For each active mobile user, a private agent is constructed in the cloud center to adaptively adjust the video quality (bit rate) by the scalable video coding technique based on the feedback of link condition. Meanwhile, the online social network interactions among mobile users are monitored by the cloud-based agents, so that the videos that are shared among users will be effectively prefetched to mobile users in advance. The adaptability of the video streaming and the effectiveness of the social-aware prefetching supported by the cloud computing are evaluated based on a prototype implementation of the framework.