We introduce a novel cache replacement policy to improve the entire network performance of video delivery over content-centric networking (CCN). In the case of the CCN structure, we argue that: 1) for video multiplexing scenario, general cache strategies that ignore the intrinsic linear time characteristic of video requests are unable to make better use of the cache resources, and 2) it is inadequate to simply extend the existing research conclusions of file-oriented popularity to chunk-by-chunk popularity, which are widely used in CCN. Unlike previous works in this field, the proposed policy in this study, named two-level popularity-oriented time-to-hold cache replacement policy (TLP-TTH), is designed on the basis of the following principles. Firstly, the proposed cache replacement strategy is customized for video delivery by carefully considering the essential auto-correlated request feature of video chunks within a video file. Furthermore, the popularity in video delivery is subdivided into two levels, namely chunk-level access probability and file-level popularity, in order to efficiently utilize cache resources. We evaluated the proposed policy in both a hierarchical topology and a real network based hybrid topology, and took viewers departure into consideration as well. The results validate that for video delivery over CCN, TLP-TTH policy improves the network performance from several aspects. In particular, we observed that the proposed policy not only increases the cache hit ratio at the edge of the network but the cache utilization at the intermediate routers is also improved markedly. Further, with respect to the video popularity variation scenario, the cache hit ratio of TLP-TTH policy responds sensitively to maintain efficient cache utilization.