For the maintenance of power lines, a core task is to diagnose the fault of different components from the aerial inspection images. Currently, deep-learning models trained on defect samples have achieved promising performances for automatic fault diagnosis. However, the slow accumulation process of fault data leads to a long-term challenge of data insufficiency in this field. In this article, a normalized multihierarchy embedding matching (NMHEM)-based anomaly detection method is proposed to inspect power line faults, which only utilizes defect-free samples during training. To impart the NMHEM with the ability to detect anomalous patterns in images, three main modules are introduced. First, the embedding generation module (EGM) is employed to extract deep hierarchical representations. Next, hierarchy-wise anomaly scores are calculated through the embedding matching module (EMM) to measure the anomalous degree, which can make the model more discriminative at different hierarchies. Finally, a normalizing module (NM) is developed and served as a credible scoring function indicating the probability of anomaly occurring, thus boosting the performance of the fault diagnosis. The proposed NMHEM adaptively aggregates local spatial and global semantic information which leverages the available nominal knowledge from normal data, achieving effective fault diagnosis of power lines. Experiments are conducted on the dataset that contains five key components. Results show that our method achieves 88.4% area under the curve (AUC) and 80.5% <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F1$ </tex-math></inline-formula> -score, which outperforms other supervised and semisupervised methods.