This paper presents a robust algorithm to reconstruct power-lines using ALS technology. Point cloud data are automatically classified into five target classes before reconstruction. In order to improve upon the defaults of only using the local shape properties of a single power-line span in traditional methods, the distribution properties of power-line group between two neighbor pylons and contextual information of related pylon objects are used to improve the reconstruction results. First, the distribution properties of power-line sets are detected using a similarity detection method. Based on the probability of neighbor points belonging to the same span, a RANSAC rule based algorithm is then introduced to reconstruct power-lines through two important advancements: reliable initial parameters fitting and efficient candidate sample detection. Our experiments indicate that the proposed method is effective for reconstruction of power-lines from complex scenarios.