In a smart city powered by the 5G network, a large amount of data never seen before will be generated. The conventional cloud computing paradigm cannot fulfil users' needs, especially for low latency. The new edge computing paradigm is emerging to mitigate the this problem. There has been some prominent research results in the field of edge computing, but most of the work is based on the assumption that edge servers have been deployed at ideal locations, and little attention has been paid to how edge servers are deployed in a geographic area. In this paper, we study how to deploy edge servers cost-effectively so that the collective area of edge servers is maximized under a certain deployment budget. In addition, there are two issues to consider in the deployment of edge servers. The first is the deployment cost, and the second is the area covered by those edge servers. For the first issue, a dynamic programming algorithm is proposed to find a solution. The key idea is to find the maximum area under a given cost. For the second issue, the geometric image approach is used to calculate the area covered by the edge server. The results of the experiments conducted on a real-world dataset demonstrate, our method is superior to several representative methods in terms of coverage maximization and running time.