Abstract: To explore the erosion damage of groundwater on rocks, the uniaxial compression creep properties of gypsum rock under different pH values and the microscopic changes of the specimens before and after acid corrosion were studied by uniaxial compression creep test and scanning electron microscope test. The results showed that the creep rate of specimens was accelerated (the stronger the acid, the faster the creep) by acid corrosion. The specimens are mainly in the form of splitting and shearing failure, and damage and failure appeared at the end (the stronger the acidity, the more obvious the damage failure was). From a microscopic point of view, the structure of the specimens in the dry state was complete, but the structure of the specimens was damaged (with the increase of acidity, increased pores and loosed structure) by acid corrosion. To describe the creep process of gypsum rock under acid corrosion conditions, the variable coefficient Abel dashpot was modified by introducing the acid corrosion degradation attenuation coefficient \beta, and the modified variable coefficient Abel dashpot was used to replace the Newton dashpot in the viscoplasticity of the Nishihara model, and a fractional creep constitutive model considering acid corrosion was established. The parameters in the model were determined through fitting of the experimental data. The sensitivity of the parameter \beta is also analyzed. The study found that the fractional derivative creep constitutive model proposed here after considering acid corrosion conditions can better reflect the three stages of creep of gypsum rock under acid corrosion, especially the accelerated creep stage.