Although 3D point cloud recognition has achieved substantial progress on standard benchmarks, the typical models are vulnerable to point cloud corruptions, leading to security threats in real-world applications. To improve the corruption robustness, various data augmentation methods have been studied, but they are mainly limited to the spatial domain. As the point cloud has low information density and significant spatial redundancy, it is challenging to analyze the effects of corruptions. In this paper, we focus on the frequency domain to observe the underlying structure of point clouds and their corruptions. Through graph Fourier transform (GFT), we observe a correlation between the corruption robustness of point cloud recognition models and their sensitivity to different frequency bands, which is measured by the GFT spectrum of the model’s Jacobian matrix. To reduce the sensitivity and improve the corruption robustness, we propose Frequency Adversarial Training (FAT) that adopts frequency-domain adversarial examples as data augmentation to train robust point cloud recognition models against corruptions. Theoretically, we provide a guarantee of FAT on its out-of-distribution generalization performance. Empirically, we conduct extensive experiments with various network architectures to validate the effectiveness of FAT, which achieves the new state-of-the-art results.