Abstract: A double medium mathematical model for coalbed methane displacement with gas injection is established. Multi-physics coupling process containing Darcy flow,adsorption/desorption and diffusion of multiple component gas and variation of porosity and permeability is involved. The model is solved numerically with finite difference method and validity of the model is verified. In example simulation calculations,improved recovery,evolution of produced gas composition and variation of coal seam properties under injection of CO₂、N₂and 70% N₂+ 30% CO₂ are contrastively analyzed. It indicates that injections of CO₂、N₂and their mixed gas are able to improve coalbed methane recovery significantly by a degree over 28 %. N₂ breaks through rapidly after injected,while CO₂ occurs in production well later. Shrinkage /swell effect plays a dominant role in variation of porosity and permeability after gas injection.Adsorption of CO₂ reduces porosity and permeability,while adsorption of N₂ leads their increase.