The wide integration of distributed generators (DGs) puts forward high requirements on the self-healing ability of distribution network. However, commonly used model-based supply restoration method depends upon accurate network parameters, which may be absent in practical operation. The rapid development of edge computing has promoted a significant change in the operation structure of distribution network. In this paper, a supply restoration method is proposed based on cloud-edge collaboration. Firstly, an intelligent decision-making model is established based on graph convolutional neural network (GCN) on the cloud, which contains network reconstruction module and power flow simulation module. The network reconstruction module is used to customize the reconstruction strategy on the cloud. After the correction by loop-breaking/loop-avoiding method, the reconstruction strategy will be sent to the edge. With the power flow simulation module, the supply recovery strategy can be determined rapidly at the edge side. Finally, the effectiveness of the proposed strategy is validated using the modified IEEE 33-node system. The results show that the proposed supply restoration strategy can effectively improve the self-healing ability of distribution network.