It is of great significance to search high-value attack sequence in complex networks, which help us easily destroy the harmful network such as crime network. Most research focuses on searching high-value nodes attack sequence, while the edge is more fragile and difficult to defend. In this paper, we deem the attacking process as a Markov process, and design a framework SHEAR (Searching High-value Edges Attack sequence through deep Reinforcement learning). During training, in the encoding module, considering that the edges are numerous and more difficult to measure, Graph neural network (GNN) is applied to automatically obtain the node embedding, and then, according to the mechanism of edge connection in the network, we propose and verify a mapping function: Hadamard, which can enlarge the similar dimensions between nodes and reduce the different dimensions between nodes, so as to retain more network information. Then the edge vector and network vector are used as the input of deep reinforcement learning (DRL). In the decoding module, we approximate the state–action value function with Q network. SHEAR can be trained on the same type of small networks and then the same model can be migrated to a wide variety of scenarios with extraordinary performance and fast speed. Compared with the best results obtained by the other four classical methods, in scenarios where attack cost is not considered, the performance of SHEAR can be improved by 33.52% in synthetic networks and 30.74% in real networks. In scenarios where removal costs are equal to edge betweenness value, SHEAR can be improved by 56.53% in synthetic networks and 38.93% in real networks. For networks with random edge weights, SHEAR can be improved by 53.87% in synthetic networks and 29.30% in real networks. In addition, we conducted further experiments to evaluate the impact of the use of graph neural networks and reinforcement learning on model performance, and found that improvements in graph representation capabilities and decision-making capabilities lead to better model performance.