With the rapid development of information and communication technologies, new services and new applications continue to emerge, especially in smart grid network scenarios. Placing services in terms of containers on the network edge is a promising solution for guaranteeing low latency, large connections, and high bandwidth. In this paper, we propose a multi-objective container migration strategy (MOCMS). Firstly, the container needed to be migrated is selected according to the resource utilization and the energy consumption condition at the network edge. Secondly, in order to avoid the problem of resource fragmentation, the node coordination matrix model is established. Thirdly, in order to obtain the optimal container migration results, an improved Binary Grey Wolf Optimizer (BGWO) algorithm is designed. Finally, the simulation results show that the proposed container migration strategy can perform better than other existing schemes.