State-of-the-art highlight removal methods still face the problems of color inconsistencies between highlight region and background, and content unreality in highlight areas. To solve these two problems, we propose a novel adaptive highlight-aware network for specular highlight removal based on an improved dichromatic reflection model. For color inconsistencies, we propose an adaptive highlight-aware (AHA) module to perceive the complete highlight information including the location and the scale of the specular highlight. Therefore, the AHA module enables the network to adaptively remove highlights while keeping non-highlight areas intact. For content unreality, we design a novel coarse-refine network to ensure that the content of the highlighted area is realistic after highlight removal. Extensive experimental results indicate that our methods can obtain excellent visual effects of highlight removal and achieve SOTA results on two datasets in several quantitative evaluation metrics. Our code is available at https://github.com/LittleFocus2201/ICASSP2024.