Automatic extraction of power lines using airborne LiDAR (Light Detection and Ranging) data has been one of the most important topics for electric power management. However, this is very challenging over complex urban areas, where power lines are in close proximity to buildings and trees. In this paper, we presented a new, semi-automated and versatile framework that consists of four steps: (i) power line candidate point filtering, (ii) local neighborhood selection, (iii) spatial structural feature extraction, and (iv) SVM classification. We introduced the power line corridor direction for candidate point filtering and multi-scale slant cylindrical neighborhood for spatial structural features extraction. In a detailed evaluation involving seven scales and four types for local neighborhood selection, 26 structural features, and two datasets, we demonstrated that the use of multi-scale slant cylindrical neighborhood for individual 3D points significantly improved the power line classification. The experiments indicated that precision, recall and quality rate of power line classification is more than 98%, 98% and 97%, respectively. Additionally, we showed that our approach can reduce the whole processing time while achieving high accuracy.