The newly rising of dynamic adaptive streaming over HTTP (DASH) enables consumers access diverse bit rate encoded video content according to the link situation, which improves the quality of experience (QoE) of consumers in mobile environment. While Content-Centric Mobile Networks (CCMNs) bring content centric design to mobile environment and has already become a promising solution for the content-based applications. The major challenges of DASH in CCMNs are how to determine proper video quality in a mobile environment and to reduce broadcasting storm. To address these problems, we design a novel adaptive video streaming solution in CCMNs (DAS-CCMN). We first analyze the load degree of content carrier, and define an interest satisfied potential (ISP) concept to reflect the ability that a content carrier can satisfy the interest request from a consumer. In DAS-CCMN, each mobile node shares its ISP information with neighbors. All nodes store this information in their interest satisfied potential table (ISPT). Based on information recorded in ISPT, a self-learning based rate determination strategy is presented to choose video content with proper bit rate. Moreover, an interest flooding control is presented to solve the broadcast storming problem for adaptive video streaming in CCMNs. Simulation results show our solution improves the performance of current DASH service in CCMNs.