The stress-dependent permeability in the heterogeneous tight sandstone has been studied based on the experiment of permeability stress sensitivity. Based on Hertz contact deformation principle，a capillary model for heterogeneous tight sandstone was established to characterize the stress sensitivity of capillary and porous media. The variation of porosity，permeability and permeability ratio under different effective stress was quantitatively analyzed. The theoretical calculation results were compared with the experimental ones as validation，and the experimental results were explained in theory. Research results show that the stress sensitivity of the heterogeneous tight sandstone is mainly presented as permeability stress sensitivity. Rock permeability varies with effective stress in different cores. The lower the rock permeability is，the faster the permeability declines. The permeability declining speed of the heterogeneous rock lies between those of the high permeability layer and the low permeability layer. When the permeability ratio increases，the stress-dependent permeability curves of heterogeneous rock are closer to that of the low permeability layer in rock. Heterogeneous tight sandstone permeability ratio becomes larger when effective stress increases.