Performance of non-line-of-sight (NLOS) ultraviolet (UV) communication is closely related with the system geometry, the communication range, and the atmospheric parameters. In this paper, we implement a full numerical analysis of the relations of path loss of NLOS UV communication with these factors using the Mie scattering theory and the Monte-Carlo method. In the numerical simulations, the actual polydisperse aerosol systems are used as the transmission medium. Since for the actual aerosol systems the atmosphere conditions may be similar within a short period, the path loss may be exclusively determined by the atmosphere visibility. Hence, we build a relation between the path loss of the communication channel and the atmosphere visibility. Simulation results reveal that for a relatively small communication range, the path loss increases with the visibility. On the other hand, low elevation of the transceiver may reduce the path loss. Our simulation results are useful for the evaluation of performance of the real NLOS UV communication systems.