An autonomous place recognition system is essential for scenarios where GPS is useless, such as underground tunnels. However, it is difficult to use existing algorithms to fully utilize the small number of effective features in underground tunnel data, and recognition accuracy is difficult to guarantee. In order to solve this challenge, an efficient point cloud position recognition algorithm, named Dual-Attention Transformer Network (DAT-Net), is proposed in this paper. The algorithm firstly adopts the farthest point downsampling module to eliminate the invalid redundant points in the point cloud data and retain the basic shape of the point cloud, which reduces the size of the point cloud and, at the same time, reduces the influence of the invalid point cloud on the data analysis. After that, this paper proposes the dual-attention Transformer module to facilitate local information exchange by utilizing the multi-head self-attention mechanism. It extracts local descriptors and integrates highly discriminative global descriptors based on global context with the help of a feature fusion layer to obtain a more accurate and robust global feature representation. Experimental results show that the method proposed in this paper achieves an average F1 score of 0.841 on the SubT-Tunnel dataset and outperforms many existing state-of-the-art algorithms in recognition accuracy and robustness tests.