Abstract: Quantitative description of permeability change in coal desorption process is an important basis for the objective understanding of nitrogen gas injection. The recovery rate of the coal sample was divided into three stages: sensitive rebound, transition rebound and slow rebound by introducing the curvature of the desorption rate, a mathematical model of permeability recovery rate considering the effect of shrinkage of coal matrix is established, and the experimental study on permeability and rebound rate of coal with different metamorphic degrees during desorption was carried out. The results show that: low rank coal permeability rebound in the process of desorption is similar to linear change with the decreasing of pore pressure, with the increase of coal metamorphic degree, permeability is increased by 2 to 3 times, and the increasing trend in the sensitive stage is more sensitive.