In unmanned aerial vehicle (UAV) flights, power lines are considered as one of the most threatening hazards and one of the most difficult obstacles to avoid. In recent years, many vision-based techniques have been proposed to detect power lines to facilitate self-driving UAVs and automatic obstacle avoidance. However, most of the proposed methods are typically based on a common three-step approach: (i) edge detection, (ii) the Hough transform, and (iii) spurious line elimination based on power line constrains. These approaches not only are slow and inaccurate but also require a huge amount of effort in post-processing to distinguish between power lines and spurious lines. In this paper, we introduce LS-Net, a fast single-shot line-segment detector, and apply it to power line detection. The LS-Net is by design fully convolutional, and it consists of three modules: (i) a fully convolutional feature extractor, (ii) a classifier, and (iii) a line segment regressor. Due to the unavailability of large datasets with annotations of power lines, we render synthetic images of power lines using the physically based rendering approach and propose a series of effective data augmentation techniques to generate more training data. With a customized version of the VGG-16 network as the backbone, the proposed approach outperforms existing state-of-the-art approaches. In addition, the LS-Net can detect power lines in near real time. This suggests that our proposed approach has a promising role in automatic obstacle avoidance and as a valuable component of self-driving UAVs, especially for automatic autonomous power line inspection.