With the mobile traffic in the network increases exponentially, multi-access edge computing (MEC) develops rapidly. MEC servers are deployed geo-distribution, which serve many mobile terminals locally to improve users' QoE (Quality of Experience). When the cache space of a MEC server is full, how to replace the cached videos is an important problem. The problem is also called the cache replacement problem, which becomes more complex due to the dynamic video popularity and the varied video sizes. Therefore, we proposed a new cache replacement scheme based on local video popularity and video size to solve the cache replacement problem of MEC servers. First, we built a local video popularity model, which is composed of a popularity rise model and a popularity attenuation model. Furthermore, the popularity attenuation model incorporates a frequency-dependent attenuation model and a frequency-independent attenuation model. Second, we formulated a utility based on local video popularity and video size. Moreover, the weights of local video popularity and video size were quantitatively analyzed by using the information entropy. Finally, we conducted extensive simulation experiments based on the proposed scheme and some compared schemes. The simulation results showed that our proposed scheme performs better than the compared schemes in terms of hit rate, average delay, and server load under different network configurations.