Using nitrogen as the blanket for the construction of a gas storage salt cavern by the solution mining under gas (SMUG) method has many advantages, such as improved safety, enhanced environmental protection and better economy. A critical issue for its field application is how to accurately predict and optimize the cavern leaching parameters when using SMUG. We propose a mathematical model for predicting leaching parameters based on the “U-tube” principle and the pressure equilibrium of liquid columns in the wellbore. We derive expressions of leaching parameters, including water injection pressure, nitrogen injection pressure, volume of nitrogen blanket, and depth of Gas-Brine (GB) interface. A calculation program is developed based on the derived equations using C# computer language. We take the JT1 cavern in Jintan district, Jiangsu province, China, as an example, and simulate the water injection pressure, nitrogen injection pressure, volume of nitrogen blanket, and depth of GB interface under different leaching rates and different de-brining pressures. The optimized leaching parameters were used in the leaching of the JT1 cavern for field tests. Compared with field monitoring data, the proposed mathematical model has high accuracy and strong reliability with an overall error of less than 3.7%, which satisfies the requirements of field cavern leaching. This study provides guidance for predicting and optimizing leaching parameters for gas storage salt cavern leaching with a nitrogen blanket.