Internet core routers are facing challenges brought by the ever-increasing transit bandwidth and routing scale. In order to meet the requirements of highly efficient packet forwarding, some solutions propose to load a small portion of the BGP RIB entries into the FIB. Therefore the most popular prefixes, which contribute major traffic loads, need to be cached in the FIB as long as possible. In this paper, we try to propose a prediction based method to cache those popular prefixes in the FIB. The cache strategy is guided by the traffic prediction of a grey model. We also apply FIB aggregation techniques to suppress the number of overlapped sub-prefixes of the popular prefixes on cache/route updates. We evaluate our method with real traffic traces and find that our prediction-based cache replacement strategy outperforms other cache strategies and matches Internet traffic dynamics very well.