To tackle problem of insufficient capability of autonomous inspection employing UAV in electricity pipe gallery without prior map, this paper proposes a UAV inspection method which is independent of prior map. In the first place, the UAV is equipped with Lidar and builds the map in real time by SLAM algorithm. The UAV searches for frontiers by RRT algorithm based on global grid map. Secondly, traditional RRT algorithm is difficult to judge integrity of map and guarantee completeness of inspection. To improve coverage, a frontier detection method based on digital image processing is proposed. Canny operator is used to detect frontiers in the map which is built in real time and evaluate completeness of the map. Finally, in order to verify effectiveness of the proposed method, simulation experiments are conducted in the model of a 220kV electricity pipe gallery which is located in Wuxi, Jiangsu province. RRT algorithm and the proposed algorithm in this paper are used to carry out autonomous inspection test respectively. The results show that the proposed algorithm can improve inspection coverage by 21.8% compared with RRT algorithm.