Gas permeability mechanism for the laminated salt rock gas storage is very complex. The key problem is to establish the permeability model and to propose the corresponding numerical method suitable for salt rock with weak interlayer based on seepage theory in porous media. An efficient and accurate method is proposed to model the flow in fracture and matrix. The fractures are regarded as boundaries among adjacent matrix blocks. Darcy’s law governs velocities in the matrix blocks, while the flow in the fracture on boundaries is set up by accounting for the fracture’s thickness. This model can reflect the fracture flow which is different from the equivalent medium model, and its computational complexity is less than that of double porous model. Combining with the field situation of Jintan gas storage in China, the pressure distributions of storage with different cyclic pressures for gas injection and production in five years are studied. It is concluded that the effect of permeability on gas pressure distribution is very important.