Abstract: The compressibility of the crack is the key factor to control permeability. Crack opening is changed by the compression, with the opening becomes smaller and the permeability is lower. Due to the long period of shale gas production, the creep characteristics of the reservoir under in-situ stress must be considered. Permeability of the cracks is related to its deformation. Based on the single-fracture cubic law and the Bandis curve of fracture deformation under normal effective stress, the fluid-solid coupling model of single fracture is derived. The paper takes the function of normal stiffness as the research core, considers the interaction of the complex environment in deep formation. Nonlinear viscoelastic-plastic model is developed to describe the shale fractures creep. It demonstrates the permeability equation with time-dependent. The assumptions are that the rock matrix is impermeable and linear elastic, and that fluid flows only in fractures. According to the flow conservation at the nodes of the fractures network, a method to calculate the permeability of the complex network is established. As an example, the stress-time related permeability model of the branch hydraulic fractured rocks is deduced. Numerical simulation method for analyzing the seepage process of the branch-shaped hydraulic fracture network is put forward. The results show that the fractures are closed unevenly under creep condition and normal closures of fractures are time-dependent. The permeability of the fractures decreases with the increasing of time, and the velocity decreases sharply in the initial stage. With the increasing of the aperture and the trace length, the permeability increases.