Unmanned aerial vehicles (UAVs) are being used to reduce the cost and risk of facility inspections. For the power distribution companies, power line inspection for providing stable power supply is an important but costly task. It includes deterioration diagnosis, detection of foreign matter adhesion, and estimation of power line-tree conflict risk, all of which is currently performed visually on foot. In this study, we explore the methods of detection and visualization of a power line-tree conflict using aerial images taken by drones. To detect a power line-tree conflict, we should firstly recognize the power lines and trees in the aerial images in order to identify the “candidate” regions of the conflict, and secondly, estimate the actual positional relationship between them in 3D. However, as previous studies have shown, the detection of power lines in an image is a challenging task because they are very narrow and monochromatic, which results in difficulty in extracting features. This specific character of the power lines could also cause failure in 3D reconstruction, in which feature matching among images is necessary. Here, we show that convolutional neural networks (CNNs) can be effectively applied in recognition of power lines and trees in an image. We also found that in mapping the candidate region of conflict to a 3D model the power line position could be estimated by taking the pole height into account. This way, even if it is difficult to reconstruct the power line in 3D, a user can make the final decision about the conflict by checking the depth and/or the height directional relationship.