Abstract Stereo image pairs can be used to improve the performance of super-resolution (SR) since additional information is provided from a second viewpoint. However, it is challenging to incorporate this information for SR since disparities between stereo images vary significantly. In this paper, we propose a parallax-attention stereo superresolution network (PASSRnet) to integrate the information from a stereo image pair for SR. Specifically, we introduce a parallax-attention mechanism with a global receptive field along the epipolar line to handle different stereo images with large disparity variations. We also propose a new and the largest dataset for stereo image SR (namely, Flickr1024). Extensive experiments demonstrate that the parallax-attention mechanism can capture correspondence between stereo images to improve SR performance with a small computational and memory cost. Comparative results show that our PASSRnet achieves the state-of-the-art performance on the Middlebury, KITTI 2012 and KITTI 2015 datasets.