Caprock sealing ability is one of the key geological factors to ensure the stable and safe operation of the underground gas storage (UGS). Gypsum salt rock is the high-quality caprock for oil and gas reservoirs, however, the effect of cyclic stress on its sealing capacity is still unclear, which restricts the construction progress of this kind of UGS. Therefore, taking the H UGS in the Sichuan Basin in China as an example, this paper analyzes the initial sealing capacity of gypsum salt caprock using cast thin section, conventional physical property test, nuclear magnetic resonance and breakthrough pressure tests. On this basis, study the variation characteristics of physical and mechanical parameters of gypsum salt caprock under cyclic stress using cyclic stress loading and unloading experiment, and then analyze the evolution law of its sealing capacity. The results show that gypsum salt caprocks of H UGS can be used as a good tight caprock with the porosity less than 1.0%, permeability less than 0.005 mD, breakthrough pressure greater than 6.0 MPa and triaxial compressive strength greater than 210 MPa. In addition, the physical properties of gypsum salt caprock become worse and the sealing capacity increases under cyclic stress, and physical and mechanical changes of gypsum salt caprock mainly occur in the first 30 cycles accounting for about 75%. Moreover, with the increase of cycles, the Poisson's ratio increases by 88% while the change range of elastic modulus is only 6.4%, indicating that gypsum salt caprocks mainly expands laterally and still maintain good elasticity. However, when the cycle times reach a certain threshold of 1002, the cumulative plastic strain of gypsum salt rock will become larger and larger until fracture. And the gypsum salt caprocks can be effective cover in the 184 cycles of loading and unloading with the maximum pressure threshold of 18 MPa and minimum pressure threshold of 1 MPa. This research results can provide theoretical guidance for cap rock stability analysis and operation parameter design of gas reservoir.