Rock salt, due to its water solubility, low permeability, high plasticity, and damage self-healing ability, is one of the best candidate rock types for underground energy storage. Utilizing salt caves to construct compressed air energy storage (CAES) facilities can effectively enhance the utilization of renewable energy. Due to the need for peak shaving, the surrounding rock of the salt cavern will undergo discontinuous cyclic loading with varying gas injection rates and pressures, namely, alternating creep-fatigue loading. Considering the actual peak-shaving cycle of a CAES plant, long-term creep-fatigue tests of rock salt with different loading cycles and stress levels were conducted. The results indicate that in long-term creep-fatigue tests for rock salt, the lower the loading stress rate is, the greater the deformation of the rock salt. The variation in the stress limit has a greater effect on creep than on fatigue loading and unloading. The deformation rate of rock salt is influenced by alterations in the stress state. Based on the test results, according to the Norton creep model, a new creep-fatigue constitutive model for rock salt was established by defining a state variable that characterizes the level of rock hardening and introducing unloading as well as crack factors. This model can accurately describe the impact of historical loading and unloading processes on the viscoplastic mechanical characteristics of rock salt. The rock salt creep-fatigue test results were used to verify the constitutive model. A comparison of the fitting curve of the different stress loading paths with the test curve reveals good consistency, indicating that the model comprehensively considers the effects of time, load, and state on rock salt creep-fatigue, effectively describing the viscoplastic deformation characteristics of rock salt under different stress paths. These research findings provide important guidance for ensuring the stability of salt caverns used for CAES.