Ultraviolet (UV) communication can work effectively in non-line-of-sight (NLOS) mode due to its special scattering property. An NLOS channel model suitable for UV communication network is established. The relationship between path loss and emission beam angle, emission elevation angle, and transmission distance is analyzed, and the effectiveness of the model is verified by experiment. Based on the established NLOS channel model, a diamond communication network design is proposed for the UV communication network, the effective coverage area expression of the diamond network and the maximum effective coverage rate of 44.23% are obtained, and the minimum number of nodes required for the complete seamless coverage of the communication network is analyzed. By comparing the diamond network and the square network under the certain connectivity, the effective coverage area loss rates of the diamond network and the square network are 1.504% and 21.083%, respectively.