Unmanned aerial vehicles (UAVs) can act as aerial base stations (BSs) to provide communication service for ground users (GUs). Especially, many UAVs can form a UAV network in an ad hoc manner, so that they can provide communication service for GUs more effectively. When deploying a UAV network consisting of multiple UAV-BSs, the UAV network needs to cover as many GUs as possible and improve the communication quality of GUs while maintaining its own connectivity. To solve this problem, a UAV network construction algorithm based on virtual force is proposed, so that a connected UAV network can be deployed to cover as many GUs as possible. On this basis, the Air-to-Air connection establishment algorithm is proposed to establish connection relationships among UAV-BSs, and the Air-to-Ground connection establishment algorithm is proposed to determine the GUs served by each UAV-BS. The UAV-BS position adjustment algorithm is further proposed, so that each UAV adjusts its own position to improve the minimum throughput of covered GUs while maintaining the connectivity of the UAV network. The proposed algorithms can be executed in a distributed manner, i.e., the UAV network can be deployed under the constrains that the positions of GUs are prior unknown and there is no central controller. The simulation results show that the algorithms proposed in this paper are superior to other baselines.