To meet the need of robust tracking in some cases (e.g., extremely illumination and thermal crossover), plenty of RGB-T tracking methods have been proposed in recent years. However, many of them can hardly meet the realtime standard since they are difficult to balance the robustness and the speed. To address such problems, we propose a new Dual Attentive Siamese Network (DASN) for RGB-T tracking. Specifically, we use a dual-stream siamese deep learning network to model tracking as a similarity measure task. In addition, to promote the information propagation procedure between two modalities and suppress the interference of background, we design the channel attention module (CAFE Module) and the channel-spatial attention module (CSAFE Module). What's more, the dual modality region proposal sub-network and the strategy of selecting proposal are constructed to boost the performance. The proposed DASN is trained end-to-end offline. Extensive experiments on three real RGB-T tracking datasets show that our tracker achieves very competive results with a high tracking speed over 140 frames per second. Code is released at https://github.com/easycodesniper-afk/SiamCSR.git.