Thanks to the advantages of low latency, high efficiency, and oneself-security, the edge computing (EC) paradigm is expected to widely be applied in a large number of scenarios. However, because EC equipment is closer to a wide variety of terminals in a realistic environment, it is also more vulnerable to terminal attacks. The security of edge computing equipment itself cannot be ignored. Docker is a lightweight container technology that closely fits the existing needs of edge computing for portability, security isolation, and convenience. In this paper, Docker technology is taken as an edge computing security support engine and a security monitoring system based on the Docker container is built. In addition, combined with container monitoring and objective weighting method, a node security judgment method is proposed. Finally, according to the results of the node security judgment, a method for evaluating the security of the unmonitored node is put forward. Consequently, an edge computing security monitoring system based on the Docker container is built, and its performance in the real environment of a smart grid system is implemented to verify the proposed method. The results prove the efficiency and security protection of the novel edge power system.