Recently, it has become a tendency to replace the work that people have been doing with the autonomous system using robots such as unmanned aerial vehicles in the structure inspection work, especially the bridge inspection section. In this paper, we propose a framework of autonomous bridge inspection using a UAV. The framework consists of a six-step process. This process starts with pre-flight for 3D mapping of the target bridge using a 3D LiDAR and RTK-GPS. Using the acquired 3D map, the user selects viewpoints (waypoints) according to the location to be inspected and plans an efficient path to connect the points. Then the preliminary preparation is completed and the structure inspection step is started. During the operation, the UAV must know its position and orientation to fly fully autonomously. Because under the bridge is a GPS-denied environment, several sensors, such as a camera, a LiDAR and an IMU, have been fused using graph structure for precise pose estimation. The precise localization of the UAV allows the data collection step to proceed smoothly. With this framework and though the actual field test, it is verified that autonomous UAV can be used for bridge inspection.