The booming of various Internet services and mobile smart terminals make the Internet paradigm shift from the traditional resource sharing to the content retrial and delivery, from host-centric to content-centric. The traditional Internet cannot satisfy the future requirements in terms of video retrieval and distribution, which spurs the researches of new network architectures such Content-Centric Networking (CCN). However, the mobility support especially the mobile provider is still an open issue with the increase of the mobile users. In this paper, we investigate the related work of mobility support of CCN in detail, and evaluate its performance under different mobile scenarios. The comparison results show that the mobile of CCN is similar to the mobile multicast, and it has good performance under the scenarios with the high content popularity and enough amounts of nodes, but needs to enhance the mobility support in the design for the high mobile scenarios.