In order to study the influence of a fault on the movement law of the overlying strata as well as its effect on the gas drainage boreholes, based on the practical situation of 1242(1) panel at Xieqiao Mine in Huainan, the Finite Element Method (FEM) model was built up, and the distribution of the stress field and the displacement field of the overlying strata in the stope with a fault were simulated by using the FEM software ANSYS. The results indicate that because of the existence of the fault, the horizontal displacement of overlying strata near the gas drainage borehole becomes larger than that in the stope without a fault, and the distribution of the stress field of the overlying strata changes greatly. When the working face is far away from the fault, the distribution of the stress field is approximately symmetrical. As the working face advances to the place 50 m away from the fault, the stress range at the right side goaf area is as twice as that at the left side.Here, the stress distribution area of goaf area and the fault plane run through, the fracture-connected-zone is formed. It can be presumed that the gas adsorbed in the coal and rock will flow into the fault zone along the fracture-connected-zone, which causes the quantity of gas drainage reduce remarkably.