Existing studies on ultraviolet (UV) non-line-of-sight (NLoS) channel modeling primarily focus on scenarios without any obstacle, which makes them unsuitable for small transceiver elevation angles in most cases. To address this issue, a UV NLoS channel model incorporating an obstacle was investigated in this paper, where the impacts of atmospheric scattering and obstacle reflection on UV signals were both taken into account. To validate the proposed model, we compared it to the related Monte-Carlo photon-tracing (MCPT) model that had been verified by outdoor experiments. Numerical results manifest that the path loss curves obtained by the proposed model agree well with those determined by the MCPT model, while its computation complexity is lower than that of the MCPT model. This work discloses that obstacle reflection can effectively reduce the channel path loss of UV NLoS communication systems.