This paper considers an emergency communication system controlling multiple unmanned aerial vehicles (UAVs) in the sky over a large-scale disaster-affected area. This system is based on delay-tolerant networking, and information from ground users is relayed by the UAVs through wireless transmission and the movement of UAVs in a store-and-forward manner. Each UAV moves autonomously according to a predetermined flight method, which uses the positions of other UAVs through communication. In this paper, we propose a new method for UAV flight considering the non-uniformity of user distributions. The method is based on the Voronoi cell using the predicted locations of other UAVs. We evaluate the performance of the proposed method through computer simulations with a non-uniform user distribution generated by a general cluster point process. The simulation results demonstrate the effectiveness of the proposed method.