Abstract: In the process of coal mining, small faults can lead to the accumulation of gas in the goaf, forming a gas enrichment zone, which poses a great threat to production safety. Therefore, it is necessary to study the gas migration law in the goaf under the influence of small faults. By using UDEC software to numerically simulate the failure process of the overlying strata in the goaf, the porosity of the overlying strata under the influence of small faults is calculated, and FLUENT software is used to numerically simulate the gas migration law in the goaf considering the influence of small faults during the mining process. Research has shown that: ① the working face is 20 m away from the small fault, and the sliding phenomenon first appears from the top of the small fault, and the displacement of the overlying rock layer in the goaf begins to be affected by the fault; When the working face reaches the fault, due to the sliding of the fault, the hanging wall rock mass undergoes a rotation phenomenon on the fault surface, supporting the rock strata in the goaf. The displacement of the overlying rock collapses significantly, and the rock strata collapse lags behind; The influence range of small faults is limited, and after the working face passes through the small fault for 60 m, the displacement law of the overlying strata in the goaf gradually returns to normal. ② By analyzing the displacement characteristics of the overlying strata in the goaf containing small faults, the displacement of the overlying strata in the goaf and its fitting formula were obtained. The three-dimensional porosity distribution law was calculated: within the range of the caving zone, the porosity of the overlying strata is the highest at four corner positions, and there is also an increase in porosity near the inlet and outlet air tunnels of the faults; Within the fracture zone, except for the position where the fault is close to the inlet and return air roadway, the porosity is relatively low and the change is not significant in other positions. ③ Obtained the gas migration law in the goaf under the influence of small faults: At a distance of 50 m from the fault in the working face, the gas migration in the goaf is almost not affected by the fault; When the working face advances to the fault, the gas migrates along the advantageous escape channel generated by the high porosity overlying rock near the fault towards the deep part of the goaf. At the same time, the gas in the hanging wall also transfers towards the deep part, causing a large amount of gas to accumulate in the lower wall of the fault, which may cause the gas to flow into the working face and return air roadway with the leakage air; When the working face passes through a fault of 50 m, the gas in the goaf continues to transfer towards the vicinity of the upper corner; When the working face passes through a fault of 100 m, the gas migration in the overlying strata of the goaf shows a turning phenomenon, and the gas concentration in the upper corner and lower wall caving zones is high.