The high-penetration integration of distributed generators (DGs) makes higher demands on the self-healing ability of a distribution network. The model-based supply restoration methods build the optimization model with accurate network parameters, which can realize the accurate formulation of restoration strategies. However, the accurate network parameters are often difficult to acquire in practical operation, which may limit the application of the model-based methods. The cloud-edge collaboration control mode can be used as an implementation scheme for fast supply restoration. A fast supply restoration intelligent decision-making method for distribution network based on cloud-edge collaboration is proposed. First, an intelligent decision-making model is established based on a graph convolutional neural network (GCN) on the cloud, containing network reconstruction and power flow simulation modules. When a failure occurs, the network reconstruction module is used to customize the reconstruction strategy on the cloud. After correction by loop-breaking/loop-avoiding method, the reconstruction strategy will be sent to the edge calculation device of distribution network edge side. With the power flow simulation module, the supply recovery strategy can be determined rapidly at the edge side to realize a fast supply restoration. Finally, the proposed strategy is analyzed using the modified IEEE 33-node system. The results show that the proposed method can effectively improve the supply restoration ability of a distribution network.