The Global Positioning System (GPS) is widely used to aid the navigation of aerial vehicles. However, the GPS cannot be used indoors, so alternative navigation methods are needed to be developed for micro aerial vehicles (MAVs) flying in GPS-denied environments. In this paper, a real-time three-dimensional (3-D) indoor navigation system and closed-loop control of a quad-rotor aerial vehicle equipped with an inertial measurement unit (IMU) and a low-cost light detection and ranging (LIDAR) is presented. In order to estimate the pose of the vehicle equipped with the two-dimensional LIDAR, an octree-based grid map and Monte-Carlo Localization (MCL) are adopted. The navigation results using the MCL are then evaluated by making a comparison with a motion capture system. Finally, the results are used for closed-loop control in order to validate its positioning accuracy during procedures for stable hovering and waypoint-following.