The creep process of the coal rock around the extraction boreholes under stress-water coupling is an important factor affecting the stability of the boreholes. To study the influence of the water content of perimeter of the coal rock around the boreholes on its creep damage, a creep intrinsic model considering water damage was established by introducing the plastic element model from the Nishihara model. To study the steady-state strain and damage evolution of coal rocks containing pores, and verify the practicality of the model, a graded loading water-bearing creep test was designed to explore the role of different water-bearing conditions in the creep process. The following conclusions were obtained: 1) water has a physical erosion and softening water wedge effect on the perimeter of the coal rock around the boreholes, which affects the loading axial strain and displacement of the perforated specimens; 2) an increase in water content reduces the time taken for perforated specimens to enter the creep phase, making the accelerated creep phase come earlier; 3) the parameters of the water damage model are considered to be exponentially related with the water content. The experimental data are similar to the results of the model parameters, and the model shows some practicality; 4) the damage variables in the accelerated creep phase increase rapidly throughout the creep process, leading to local instability in the borehole. The findings of the study provide important theoretical implications for the study of instability in gas extraction boreholes.