Stereo matching is a fundamental building block for many vision and robotics applications. An informative and concise cost volume representation is vital for stereo matching of high accuracy and efficiency. In this paper, we present a novel cost volume construction method which generates attention weights from correlation clues to suppress redundant information and enhance matching-related information in the concatenation volume. To generate reliable attention weights, we propose multi-level adaptive patch matching to improve the distinctiveness of the matching cost at different disparities even for textureless regions. The proposed cost volume is named attention concatenation volume (ACV) which can be seamlessly embedded into most stereo matching networks, the resulting networks can use a more lightweight aggregation network and meanwhile achieve higher accuracy, e.g. using only 1/25 parameters of the aggregation network can achieve higher accuracy for GwcNet. Furthermore, we design a highly accurate network (ACVNet) based on our ACV, which achieves state-of-the-art performance on several benchmarks.