In order to study the characteristics of fault slip instability when the 6305 working face of Xinjulong Coal Mine passes through the graben structure area, based on the numerical simulation, the stress characteristics and evolution law of the fault surface in the graben structure area under the influence of mining are analyzed, and the slip process of the fault in the graben structure area is analyzed according to the fault slip tendency index TS. The results show that the stability of fault plane is more sensitive to shear stress during the advancing process of 6305 working face, and the change of shear stress plays a leading role in the change of fault slip tendency TS. In the graben tectonic area, FL37 and FL39 faults slip stage by stage. FL37 fault slips first near the overburden area, and then the slip area gradually evolves from the high rock layer to the low rock layer. In contrast, FL39 fault slips first near the coal seam area, and the slip area evolves from the low rock layer to the high rock layer. In the process of working face crossing the graben structure area, the risk of mining fault slip induced impact in the graben structure area is greater than that in the graben structure area. The research results have certain reference significance for the safe mining of working face under similar conditions.