To detect and locate the corona discharge of insulators quickly in unmanned aerial vehicle (UAV) power line inspection, a corona detection and location method for power lines in a UAVs track was investigated. First, the corona discharge power detection model was analyzed and established, and a formula for ultraviolet radiation power from a discharge source was obtained. Then, a corona detection device with high sensitivity was designed, and a positioning method for finding insulator defects in a UAVs track was developed. This method was used to detect the power line tower from two different angles. By comparing the two detection results, the position of the defective insulator could be determined. Finally, a method for electro spark and ultraviolet (UV) light-emitting diode (LED) detection based on location was designed. The results show that the detector can accurately detect the ultraviolet power produced by a spark. Influenced by the loss of UV light in the air, the measured value decreases with the increase of distance, and the relative error is within 11.5% at different distances. In the UV LED detection experiment, the measured values are more accurate when the detection angles are selected as 0° and 15°. In general, the method is accurate and effective in the detection of weak corona discharge, and it can meet the positioning requirements for defective power line insulators in a UAVs track.