In order to accurately predict the shale gas productivity and guide the actual production，in the consideration of the permeability change caused by rock deformation and the viscous flow，surface diffusion and Knudsen diffusion of shale gas，and by coupling the geomechanical effect with the fluid flow，a mathematical model that comprehensively considers the stress sensitivity and the various percolation mechanisms of shale gas was proposed. The discrete fracture model was used to describe the microfractures and hydraulic fractures in the formation，and it was solve by finite element method. The results show that surface diffusion and Knudsen diffusion increase shale permeability and further increase the shale gas production. The stress-sensitive effect reduces the matrix permeability，resulting in a decrease in cumulative gas production.The larger surface diffusion coefficient and the Langmuir volume or the lower bottom hole pressure would increase the cumulative gas production of shale gas. For the shale gas reservoirs with a larger Langmuir volume，it is beneficial to reduce the pressure at the bottom of the well to reach a higher production potential. The simulation results of the model fit well with the actual historical production data，which verifies the correctness of the model.