Abstract: In order to study the progressive failure limit instability problem of gas-bearing coal, this paper analyzes the strength reduction limit safety factor and the progressive failure limit instability process of gas-bearing coal based on the strength reduction method of gas-bearing coal and with the help of finite element numerical simulation software. The research results show that the strength reduction parameter correction of gas-containing coal can characterize the weakening effect of gas on the coal body, and it is suitable for analyzing the limit instability process of coal body progressive failure in numerical simulation software; the strength reduction limit safety factor is affected by surrounding rock and gas pressure, external load, coal Poisson’s ratio and other factors, the smaller the limit safety factor value, the easier it is for the coal body to reach the unstable failure state; in the process of strength reduction, the state evolution of gas-containing coal is divided into initial damage, progressive failure, limit instability three stages.