To achieve damage detection of three-dimensional structures using UAVs while avoiding collisions between the UAV and the structure, and ensuring the accuracy and efficiency of the inspection process, this paper proposes a full-coverage path planning method for UAVs based on Graph Transformer. The problem is treated as a variant of the traveling salesman problem and is solved using a graph neural network (GNN) on a fully connected graph. An attention module is introduced in the GNN to alleviate the limitations of sparse message passing in the network. The method combines graph convolution and attention mechanisms to extract features from nodes and edges. In the decoder, the probability of each edge being part of the solution is evaluated to generate a probability heatmap. An initial solution is obtained using beam search, which is then optimized through local search. Experimental results show that, compared to deep learning methods based on reinforcement learning and search, as well as improved ant colony optimization and genetic algorithms, the proposed method has significant advantages in terms of performance and generalization. It is also applicable to both Euclidean and non-Euclidean distances in two-dimensional and three-dimensional spaces, demonstrating great potential in UAV navigation and full-coverage path planning.