Robotic dexterous grasping is the first step to enable human-like dexterous object manipulation and thus a crucial robotic technology. However, dexterous grasping is much more under-explored than object grasping with parallel grippers, partially due to the lack of a large-scale dataset. In this work, we present a large-scale robotic dexterous grasp dataset, DexGraspNet, generated by our proposed highly efficient synthesis method that can be generally applied to any dexterous hand. Our method leverages a deeply accelerated differentiable force closure estimator and thus can efficiently and robustly synthesize stable and diverse grasps on a large scale. We choose ShadowHand and generate 1.32 million grasps for 5355 objects, covering more than 133 object categories and containing more than 200 diverse grasps for each object instance, with all grasps having been validated by the Isaac Gym simulator. Compared to the previous dataset from Liu et al. generated by GraspIt!, our dataset has not only more objects and grasps, but also higher diversity and quality. Via performing cross-dataset experiments, we show that training several algorithms of dexterous grasp synthesis on our dataset significantly outperforms training on the previous one. To access our data and code, including code for human and Allegro grasp synthesis, please visit our project page: https://pku-epic.github.io/DexGraspNet/.