The permeability stress-sensitivity of formation rock is one of the most important research subjects in the petroleum industry and geotechnical industry. A capillary tube-pore network flow model is presented in order to explain permeability stress-sensitivity based on permeability stress-sensitivity experiments. The new model fully considers the complex connectivity among pore throats, pore structure tortuosity, different types and sizes of pore throats, and their different contribution ratios to the rock permeability. When effective stress is loaded on the low permeability rock samples, the larger pore throats, as the main flow channel, are firstly compressed smaller. Therefore, both fluid flow resistance and pore tortuosity simultaneously increase; it is the main reason that the rock permeability dramatically declines in the initial period for increasing effective stress. Since there are less large pore throats in the rock with lower permeability, those larger pore throats compressed smaller could have a greater impact on the rock permeability. Therefore, the smaller the rock initial permeability is, the stronger its stress-sensitivity is. Comparing with the experimental results for pore structure deformation, the new model is very reasonable for explaining the permeability stress-sensitivity of low permeability rock.