Triaxial compression creep tests were performed on salt rock samples using cyclic confining pressure with a static axial pressure. The test results show that, up to a certain time, changes in the confining pressure have little influence on creep properties of salt rock, and the axial creep curve is smooth. After this point, the axial creep curve clearly fluctuates with the confining pressure, and is approximately a straight line both when the confining pressure decreases and when it increases within one cycle period. The slope of these lines differs: it is greater when the confining pressure decreases than when it increases. In accordance with rheology model theory, axial creep equations were deduced for Maxwell and Kelvin models under cyclic loading. These were combined to establish an axial creep equation for the Burgers model. We supposed that damage evolution follows an exponential law during creep process and replaced the apparent stress in creep equation for the Burgers model with the effective stress, the axial creep damage equation for the Burgers model was obtained. The model suitability was verified using creep test results for salt rock. The fitting curves are in excellent agreement with the test curves, so the proposed model can well reflect the creep behavior of salt rock under low-frequency cyclic loading. In particular, it reflects the fluctuations in creep deformation and creep rate as the confining pressure increasing and decreasing under different cycle periods.