In this paper, we tackle the problem of grasping transparent and specular objects. This issue holds importance, yet it remains unsolved within the field of robotics due to failure of recover their accurate geometry by depth cameras. For the first time, we propose ASGrasp, a 6-DoF grasp detection network that uses an RGB-D active stereo camera. ASGrasp utilizes a two-layer learning-based stereo network for the purpose of transparent object reconstruction, enabling material-agnostic object grasping in cluttered environments. In contrast to existing RGB-D based grasp detection methods, which heavily depend on depth restoration networks and the quality of depth maps generated by depth cameras, our system distinguishes itself by its ability to directly utilize raw IR and RGB images for transparent object geometry reconstruction. We create an extensive synthetic dataset through domain randomization, which is based on GraspNet-1Billion. Our experiments demonstrate that ASGrasp can achieve over 90% success rate for generalizable transparent object grasping in both simulation and the real via seamless sim-to-real transfer. Our method significantly outperforms SOTA networks and even surpasses the performance upper bound set by perfect visible point cloud inputs.Project page: https://pku-epic.github.io/ASGrasp