Topology information is the basic information to promote the intelligent operation of the distribution networks. However, the incomplete historical topology information greatly restricts the operation control of the power distribution networks. There is an urgent demand for innovative methods of topology identification. In this paper, an edge computing-based topology identification method for low voltage power distribution networks is studied. The edge computing devices collect the electricity consumption data from the user’s smart meter. The data dimension is reduced using principal component analysis to obtain the topological connection relationship between nodes. The T-type grey correlation method is used to revise the mistake caused by the principal component analysis, improving the accuracy while ensuring the speed of topology identification. Finally, the accuracy and performance of the proposed method are verified by a typical test feeder. The results show that the proposed method achieves an accuracy of 100% if enough data is provided and it remains an accuracy of at least 90% with 12 groups of data.