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Previous few-shot learning (FSL) works mostly are limited to natural images of general concepts and categories. These works assume very high visual similarity between the source and target classes. In contrast, the recently proposed cross-domain few-shot learning (CD-FSL) aims at transferring knowledge from general nature images of many labeled examples to novel domain-specific target categories of only a few labeled examples. The key challenge of CD-FSL lies in the huge data shift between source and target domains, which is typically in the form of totally different visual styles. This makes it very nontrivial to directly extend the classical FSL methods to address the CD-FSL task. To this end, this paper studies the problem of CD-FSL by spanning the style distributions of the source dataset. Particularly, wavelet transform is introduced to enable the decomposition of visual representations into low-frequency components such as shape and style and high-frequency components e.g., texture. To make our model robust to visual styles, the source images are augmented by swapping the styles of their low-frequency components with each other. We propose a novel Style Augmentation (StyleAug) module to implement this idea. Furthermore, we present a Self-Supervised Learning (SSL) module to ensure the predictions of style-augmented images are semantically similar to the unchanged ones. This avoids the potential semantic drift problem in exchanging the styles. Extensive experiments on two CD-FSL benchmarks show the effectiveness of our method. Our codes and models will be released.