Coal seam with low permeability is widely distributed in China. Injection of flue gas (N2:CO2 = 0.85:0.15) is an effective approach to improve coal seam gas drainage efficiency. This process relates complex responses among ternary gases (CH4, CO2, and N2) competitive sorption on coals, gas diffusion, gas‐water migration by means of two‐phase flow, and coal deformation. In this paper, an improved hydraulic‐mechanical model coupling above interactions is established for flue gas injection enhanced gas drainage. This model is used to simulate flue gas enhanced drainage by finite element method. The sensitivity analyses of key factors are made to recovery a better understanding on the processes controlling flue gas enhanced drainage. Results show that the flue gas enhanced drainage can indeed improve the efficiency of gas extraction and reduce the gas pressure to the required value in a shorter duration. Due to the competitive adsorption and gas sweeping effect of injected flue gas, CH4 is driven toward drainage borehole, and CH4 pressure and content near the injection borehole decrease faster than that near the drainage borehole. The peak CH4 pressure laterally moves from the injection borehole to the drainage borehole. Higher injection pressure, initial permeability, and smaller sorption affinity ratios may lead to greater CH4 production rate at early drainage stage, but smaller CH4 production rate at late stage. The factors controlling the behavior of flue gas enhanced drainage are initial permeability, injection pressure, and sorption affinity ratios in order. This work offers useful framework to investigate important technical challenges associated with enhanced mine gas drainage, as well as unconventional gas development.