For a large object, scanning from the air is one of the most efficient methods of obtaining 3D data. In the case of large cultural heritage objects, there are some difficulties in scanning with respect to safety and efficiency. To remedy these problems, we have been developing a novel 3D measurement system, the Floating Laser Range Sensor (FLRS), in which a range sensor is suspended beneath a balloon. The obtained data, however, have some distortions due to sensor-movements during the scanning process. In this paper, we propose a method to recover 3D range data obtained by a moving laser range sensor. This method is applicable not only to our FLRS, but also to a general moving range sensor. Using image sequences from a video camera mounted on the FLRS enables us to estimate the motion of the FLRS without any physical sensors such as gyros or GPS. In the first stage, the initial values of camera motion parameters are estimated by full-perspective factorization. The next stage refines camera motion parameters using the relationships between camera images and range data distortion. Finally, by using the refined parameters, the distorted range data are recovered. In addition, our method is applicable with an uncalibrated video camera and range sensor system. We applied this method to an actual scanning project, and the results showed the effectiveness of our method.