Although a UAV itself is adaptable to variety of tasks, its low payload and short flight time limit its usage. As a way to overcome the limitations of a UAV, a multi-UAV system is being researched. In order to utilize the Multi-UAV system, it is essential to estimate the relative position of each UAV. In this paper, a relative position estimation method is proposed that requires only range measurements from each pair of UAV combinations. The positions of UAVs are estimated by minimizing the difference between the range measurements and the distance values which are calculated from each pair of estimated positions of UAVs. The performance of the proposed method is verified by five UAVs flight simulation. The range data are generated from the ground-truth positions of five UAVs and Gaussian noise added range data are used for the experiments.