Abstract: The change of effective stress in the periodic injection-production process of underground gas storage will cause stress sensitivity of the reservoir. In order to understand the influence of stress sensitivity on permeability of gas storage reservoir and to provide the basis for optimizing the injection and production system of gas storage, stress sensitivity tests with consideration of effective stress action duration and without were carried out on carbonate rock samples, and the permeability of the rock samples in the test process were tested. By means of scanning electron microscope (SEM), the fracture wall of rock samples before and after the test considering the effective stress action duration was observed. The test results show that the stress sensitivity of carbonate fractures and matrix rock samples is weak–moderately weak and none without consideration of action duration, while the stress sensitivity of fracture and matrix rock samples considering the effective stress action duration is moderately strong–strong and weak. With the increase of effective stress action duration, the breaking of micro-protrusions on rock fracture walls and the initiation and propagation of micro-fractures will strengthen the stress sensitivity of rock samples. The results show that for the purpose to weaken the stress sensitivity of underground gas storage, the injection-production pressure of underground gas storage should be controlled reasonably.