The drastic increase of mobile video traffic has resulted in communication delay and slow download speed. In the 5G wireless networks, caching or prefetching video at mobile edge servers can take advantage of the high-speed local link to alleviate the load of the core network. However, the tradeoff between data prefetching and cache replacement strategy is still a challenge in Mobile-edge computing networks, especially when the users are mobile and cache size is constrained. To address this, we design a mobility-aware utility function based on the user's moving probability and the popularity of video clips. Then, we formulate the optimization problem as an integer linear programming (ILP)with a set of knapsack constraints to develop an efficient dynamic programming algorithm. Compared with the baseline algorithm, the results of simulation experiment show that our approach can not only raise the hit rate by 24.93%, but also control the cost effectively. In the meantime, video distortion reduction is increased by 21.26% on average as well.