Aiming at the stress sensitivity problem of tight reservoirs with different microfractures, the cores of H oilfield and J oilfield with different microfractures were obtained through the fractures experiment, so as to study the change of gas permeability in tight sandstone core plug during the change of confining pressure. Besides, we use the nuclear magnetic resonance (NMR) spectra of the core before and after saturation to verify whether the core has been successfully fractured. Based on Terzaghi’s effective stress principle, the permeability damage rate (D) and the stress sensitivity coefficient (Ss) are used to evaluate the stress sensitivity of the core, which show consistency in evaluating the stress sensitivity. At the same time, we have studied the petrological characteristics of tight sandstone in detail using thin section (TS) and scanning electron microscope (SEM). The results show that the existence of microfractures is the main factor for the high stress sensitivity of tight sandstone. In addition, because of the small throat of the tight reservoir core, the throat closes when the overlying stress increases. As a result, the tight sandstone pore size is greatly reduced and the permeability is gradually reduced. Therefore, in the development of tight reservoirs, we should not only consider the complex fracture network produced by fracturing, but also pay attention to the permanent damage of reservoirs caused by stress sensitivity.