By using conventional meteorological data, satellite data, radar data and NCEP reanalysis data, the instability formation process of a torrential rainfall from Taiyuan to Shijiazhuang on 9 July 2013 is studied. The results show that the torrential rainfall near Taiyuan occurred after light stratiform precipitation existed for six hours. The convective precipitation with weak thunder and lightning was embedded in the stratiform and it was located behind the cold front, more than 120 km away from surface front. Such cold sector torrential rainfall is easy to be missed. From 08:00 BT to 14:00 BT, depth of planetary boundary layer (PBL) cold air was continuously deepening, the dry and cold air mass with low pseudoequivalent potential temperature extended from northeast to southwest, and the unstable atmosphere was situated over the stable boundary layer, so the torrential rain was caused by elevated convection. The northeast wind at 850 hPa and the southwest wind at 500 hPa were strengthened at the same time, baroclinicity of frontal zone got stronger, the atmospheric stratification was transformed from absolute stability, which was almost neutral, to potential instability by the dry advection in 400-500 hPa and was moistened at lower level by frontal lifting. The potential unstable layer changed to conditional unstable layer by the frontal lifting of warm and humid air layer. In the afternoon, the atmosphere was absolutely stable near Shijiazhuang.