Achieving human-like dexterous manipulation remains a crucial area of research in robotics. Current research focuses on improving the success rate of pick-and-place tasks. Compared with pick-and-place, throw-catching behavior has the potential to increase picking speed without transporting objects to their destination. However, dynamic dexterous manipulation poses a major challenge for stable control due to a large number of dynamic contacts. In this paper, we pro- pose a Stability-Constrained Reinforcement Learning (SCRL) algorithm to learn to catch diverse objects with dexterous hands. The SCRL algorithm outperforms baselines by a large margin, and the learned policies show strong zero-shot transfer performance on unseen objects. Remarkably, even though the object in a hand facing sideward is extremely unstable due to the lack of support from the palm, our method can still achieve a high level of success in the most challenging task.