When handling occlusion in unsupervised stereo matching, existing methods tend to neglect the supportive role of occlusion and to perform inappropriate disparity smoothing around the occlusion. To address these problems, we propose an occlusion-aware stereo network that contains a specific module to first estimate occlusion as an additional depth cue. In the occlusion inference module, a pixel is classified with a three-category label based on whether an area is occluded by an object on the left, occluded by an object on the right, or unoccluded. After the occluders are detected, we introduce a directed disparity smoothing loss that allows valid disparity estimates to be propagated to fill the occluded region, while ambiguous matches in the occluded region do not affect other regions. Disparity and occlusion are trained alternately in an unsupervised manner with detached backpropagation to enable the directed smoothness. Experiments show that our method achieves 3-pixel threshold error rates of 6.51% and 5.69% on the KITTI 2015 and KITTI 2012 validation sets, state-of-the-art results among unsupervised learning networks at the time of submission.