There are few studies on the stress sensitivity of reservoirs at the micropore structure level. A porous carbonate core of the fourth member of the Sinian Dengying formation gas reservoir in Central Sichuan is selected to conduct an in-situ submicron CT permeability stress sensitivity test. The experimental results show that the permeability of porous carbonate rock decreases obviously with the increase of effective stress. Increasing effective stress decreases the pore volume, pore throat diameter, and throat length. The probability distribution of the shape factor curve shifts to the right, while the diameter of the pore throat distribution curve and the throat probability distribution curve of the core shift to the left. In different pressure stages, it has different effects on different sizes and shapes of pores. For micro pores and throats, the damage is obvious, and the connectivity of the pore throat becomes poor. The change in pressure causes a change in the core micropore structure, which leads to the decline of core permeability. With the decrease of effective stress, the core permeability cannot be restored, which indicates that the damage caused by stress sensitivity is irreversible.