Recently, during 15–17 June 2021, an extreme rainstorm occurred on the northern slope of Kunlun mountain in southern Xinjiang, China. After considering the effects of geography on the rainstorm, a terrain-following, nonhydrostatic generalized vertical motion equation was built under Boussinesq approximation and terrain-following governing equations. Diagnostic results indicated that the three main forcing terms stimulating vertical motion development during the rainstorm were meridional pressure gradient force coupled with meridional divergence (first term), vertical pressure gradient force coupled with zonal divergence (second term), and meridional gradient of diabatic heating (third term). The first term reflected that the gradually increased northern flow led to the growth of meridional convergence under the blockage of Kunlun mountain, which activated the ascending motion. The lead forcing process for the convection was the meridional convergence, followed by zonal convergence. Meridional and vertical pressure gradients had an amplification effect on the first two terms in a terrain-following coordinate frame. The meridional gradient of diabatic heating was intensified by the water vapor convergence and diabatic heating processes during the convection development stage, thereby promoting the ascending motion. Westerly winds over the Kunlun mountain exhibited evident wave characteristics in the middle and upper troposphere under the influence of geography. The convection in the Kunlun mountain windward slope was strengthened by the upper divergence induced by a gravity wave. Thus, the rainstorm in southern Xinjiang was caused by the combined effects of meridional and zonal convergences, diabatic heating, and gravity wave activities.