In order to implement the tasks on the various environments such as unknown or dangerous environments, unmanned aerial vehicles (UAVs) are being researched. However, for a single UAV, the tasks are restricted owing to the low payload and short flight time. With the aim of overcoming the limitation of a single UAV, the multi-UAV system is being researched. Meanwhile, to utilize the multi-UAV system efficiently, it is important to estimate the relative position of each UAV. Without the global navigation satellite system (GNSS), the vision-based relative position estimation methods such as image matching are widely used. However, sharing the vision data is unsuitable for the multi-UAV system because of its high communication bandwidth load. In this study, we propose a novel ultra-wideband (UWB) and odometry fusion method that shares odometry and range data which have significantly smaller size compared with the image data to estimate the relative position between the UAVs.