Stairs are common building structures in urban environments, and stair detection is an important part of environment perception for autonomous mobile robots. Most existing algorithms have difficulty combining the visual information from binocular sensors effectively and ensuring reliable detection at night and in the case of extremely fuzzy visual clues. To solve these problems, we propose a neural network architecture with RGB and depth map inputs. Specifically, we design a selective module, which can make the network learn the complementary relationship between the RGB map and the depth map and effectively combine the information from the RGB map and the depth map in different scenes. In addition, we design a line clustering algorithm for the postprocessing of detection results, which can make full use of the detection results to obtain the geometric stair parameters. Experiments on our dataset show that our method can achieve better accuracy and recall compared with existing state-of-the-art deep learning methods, which are 5.64% and 7.97%, respectively, and our method also has extremely fast detection speed. A lightweight version can achieve 300 + frames per second with the same resolution, which can meet the needs of most real-time detection scenes.