In general, deep learning-based fault diagnosis methods need a large number of training samples, which are often not available in real applications. Aiming at this problem, this article develops a new data augmentation method, i.e., randomized wavelet expansion (RWE), to generate a set of synthesis samples that share similar characteristics with the original sample. The first key point is that the amplitudes of wavelet coefficients at a randomly selected frequency band are enlarged through random expansion. Another key point is that the synthesis samples are processed to have the same mean values and standard deviations as their corresponding original sample. Afterward, the synthesis samples are used as the training dataset to train a deep convolutional neural network (CNN) for implementing the few-shot fault diagnosis of aviation hydraulic pumps. Finally, the performance has been validated through a series of experiments.