Many deep-learning methods have been developed for fault diagnosis. However, due to the difficulty of collecting and labeling machine fault data, the datasets in some practical applications are relatively much smaller than the other big data benchmarks. In addition, the fault data come from different machines. Therefore, on some occasions, fault diagnosis is a multidomain problem with small data, where satisfactory transfer performance is difficult to obtain and has been rarely explored from the few-shot learning viewpoint. Different from the existing deep transfer learning solutions, a novel transfer relation network (TRN), combining a few-shot learning mechanism and transfer learning, is developed in this study. Specifically, the fault diagnosis problem has been treated as a similarity metric-learning problem instead of solely feature weighted classification. A feature net and a relation net have been, respectively, constructed for feature extraction and relation computation. The Siamese structure has been borrowed to extract the features of the source and the target domain samples with shared weights. Multikernel maximum mean discrepancy (MK-MMD) is employed on several higher layers with different tradeoff parameters to enable an efficient domain feature transfer considering different feature properties. To implement efficient diagnosis based on small data, an episode-based few-shot training strategy is adopted to train TRN. Average pooling has been adopted to suppress the noise influence from the vibration sequence which turns out to be important for the success of time sequence-based fault diagnosis. Transfer experiments on four datasets have verified the superior performance of TRN. A significant improvement of classification accuracy has been made compared with the state-of-the-art methods on the adopted datasets.