The clinical treatment of degenerative and developmental lumbar spinal stenosis (LSS) is different. Computed tomography (CT) is helpful in distinguishing degenerative and developmental LSS due to its advantage in imaging osseous and calcified tissues. However, boundaries of the vertebral body, spinal canal and dural sac have low contrast and are hard to identify in a CT image, so the diagnosis depends heavily on the knowledge of expert surgeons and radiologists. In this paper, we develop an automatic lumbar spinal CT image segmentation method to assist LSS diagnosis. The main contributions of this paper are as follows: 1) a new lumbar spinal CT image dataset is constructed that contains 2393 axial CT images collected from 279 patients, with the ground truth of pixel-level segmentation labels; 2) a dual densely connected U-shaped neural network (DDU-Net) is used to segment the spinal canal, dural sac and vertebral body in an end-to-end manner; 3) DDU-Net is capable of segmenting tissues with large scale-variant, inconspicuous edges (e.g., spinal canal) and extremely small size (e.g., dural sac); and 4) DDU-Net is practical, requiring no image preprocessing such as contrast enhancement, registration and denoising, and the running time reaches 12 FPS. In the experiment, we achieved state-of-the-art performance on the lumbar spinal image segmentation task. We expect that the technique will increase both radiology workflow efficiency and the perceived value of radiology reports for referring clinicians and patients.