In the field of computer vision, disparity estimation from a pair of images has been one of the most popular directions. Although matching methods based on deep learning have made significant progress, there are still challenges in the field: dealing with non-Lambertian materials and estimating the disparity of objects with specular reflections. To solve the problem of stereo matching of objects with specular reflections, we propose a method by cascading a network that removes specular light, a specular-free refinement network, and a stereo matching network CREStereo loaded with pretrained model that performs well on a large number of tasks. This achieves effective suppression of specular light and accurate disparity estimation. In addition, we specially propose two novel datasets, which contain images of specular objects under strong light observed from multiple viewing angles, accurate and dense disparity ground truth labels of the corresponding images, and corresponding images without strong light illumination. We performed joint supervised training on our network’s ability to suppress specular light and estimate disparity, and the experimental results demonstrate the effectiveness of the datasets and the proposed method is quite competitive.