Permeability stress-sensitivity is the critical characteristic in reservoir development, especially for coalbed methane (CBM) reservoir. To investigate the permeability evolution during production in Shouyang CBM reservoir, Qinshui Basin, China, a new stress-sensitive permeability analytical model is proposed, while a time-lapse three-dimensional (4D) multi-physical coupling model is constructed. Heterogeneity and anisotropy of the reservoir flow and geomechanical properties as well as the permeability stress-sensitivity are adequately considered in the model. A coupling method is proposed to bridge data between finite difference (FD) grids and finite element (FE) grids with an interface code complied by Python. The reservoir flow data and geomechanical data are connected with each other by the interface code. Permeability stress-sensitivity experiments are carried out and compared with the numerical simulation results. According to the dynamic simulation results of 230 producing days, the stress increases with pore pressure decline, and the permeability stress-sensitivity is very strong in Shouyang 15# coalbed, especially in the initial stage of compression. The dynamic evolutions of stress and permeability are significantly affected by the anisotropy and heterogeneity of coalbed during depletion. The proposed stress-dependent permeability model is more suitable for characterizing the permeability evolution of the Shouyang CBM reservoir.