In actual industrial scenarios, fault data is rare and fault labels are difficult to obtain, which brings many obstacles for fault diagnosis. For this situation, this research proposes a novel semi-supervised convolutional sparse filter with local mechanism similarity regularization (CSF-LMSR) to construct a more reliable few-shot diagnosis method for power transformer. First, a sparse filter with local mechanism similarity regularization term (SF-LMSR) is designed as a more interpretable unsupervised feature extractor with prior knowledge. This unsupervised process enables the model to extract satisfactory features from the whole dataset even with a lower proportion of labeled data. Second, SF-LMSR is combined with convolutional neural network (CNN) by a novel coupling mode of kernel replacement, which enhances the learning ability of CNN. This classification model still adopts supervised learning training, but the demand for labeled fault data is greatly reduced, which reduces the burden of labels. The effectiveness of the proposed method is verified using real power transformer dissolved gas analysis (DGA) datasets. It can be seen from experimental results that the proposed method does provide a new perspective for transformer fault diagnosis, and it is a successful attempt for the power industry few-shot diagnosis problem.