The power lines and equipment of power system are inspected regularly by Unmanned Aerial Vehicles (UAVs) and video monitoring devices, which generates large quantities of power inspection images. The deep learning (DL) methods, such as visual classification and detection models, can process such images effectively. However, due to the data privacy regulations, the inspection images collected by a power company are not allowed to be shared with others. The data from a single owner is limited not only in quantity but also in type, which cannot always support to train a high-performance model. In this work, we propose a federated learning (FL) based method for processing power inspection images, which allows different data owners to cooperatively train visual classification and detection models without sharing their local images. To improve the training efficiency, we further propose a Federated Round-level Momentum (FedRM) method by adding a momentum term during the aggregation of model weights. We demonstrate the proposed method in three real-world power inspection image datasets for visual classification, object detection and defect detection tasks respectively, and the effects of non-independent and identically distributed (Non-IID) data on the FL based models are investigated. The results show that the performance of the FL models for power inspection images is higher than that of local trained models. It is also verified that our proposed FedRM method improves the FL-training efficiency significantly, which could reach at most 5×, 3.7×, and 6.8× speedup on visual classification, object detection, and defect detection tasks respectively.