To obtain the accurate time difference of arrival (TDOA) and frequency difference of arrival (FDOA) for passive localization in an unmanned aerial vehicle (UAV) swarm, UAV swarm network synchronization is necessary. However, most of the traditional distributed time synchronization protocols are based on iteration, which hinders efficiency improvement. High communication costs and long convergence times are often required in large-scale UAV swarm networks. This paper presents a neighborhood selection-all selection (NS-AS) synchronization mechanism-based moving source localization method for UAV swarms. First, the NS-AS synchronization mechanism is introduced, to model the UAV swarm network synchronization process. Specifically, the UAV neighbors are first grouped by sector, and the most representative neighbors are selected from each sector for the state update calculation. When the UAV swarm network reaches a fully connected state, the synchronization mechanism is switched to select all neighbors, to improve the convergence speed. Then, the TDOA-FDOA joint localization algorithm is employed to locate the moving radiation source. Through simulation, the effectiveness of the proposed method is verified by the system convergence and localization performance under different parameters. Experimental results show that the synchronization mechanism based on NS-AS effectively improves the convergence speed of the system while ensuring the accuracy of moving radiation source localization.