With the explosion of data volume, it becomes challenging to deliver high quality service to mobile users. Therefore, edge caching has received significant attentions since it can bring contents near mobile users, to boost spectral efficiency, and reduce backhaul load of mobile networks. Due to limited storage resources within mobile networks, it is important to improve efficiency of content management in edge caching. In this article, we propose an integrated content-centric mobile network framework for edge caching in 5G networks, which can leverage content-centric networking (CCN), achieve content-oriented information management, and increase content delivery efficiency. We elaborately design the cache-enabled mobile network architecture, CCN based function entities, CCN embedded protocol stack, and content retrieval process, and develop several effective approaches for tackling practical implementation constraints of CCN based edge caching. We demonstrate that our content caching strategies can significantly enhance edge caching performance. To further improve the performance of content-centric mobile edge caching, we identify promising open research directions.