Abstract: Most existing study on non-line-of-sight solar-blind ultraviolet communication single scatter models use the prolate-spheroidal coordinates to obtain solutions. In the solving process, the effective scattering volume must undergo the difficult numerical integration and the three groups of integral limits which determine the volume can be calculated. The widely adopted yet complex single-scatter channel model is significantly simplified by means of a closed-form expression for tractable analysis in this paper. And the path loss is given as a function of transceiver geometries as well as scattering and absorption coefficient. The simulation results of transmission distance and path loss show that the approximated path loss matches that from direct numerical integration very well. Using the closed-form expression of path loss, the influence of atmospheric visibility on the path loss and bit-error-rate of the ultraviolet communication system is simulated. The simulation results show that: the better weather and the higher visibility do not result in greater system performances, but when the visibility equals 9-10 km, the best performance can be obtained.