In order to study the creep characteristics of sandstone, the conventional triaxial and creep experiments of the sample under 10MPa confining pressures were carried out by using the full-automatic triaxial servo. On this basis, in order to simulate the whole creep process effectively, a nonlinear creep model with fractional derivatives is proposed and verified. The results show that the cyclic creep rate and axial creep rate of the specimens are close at the creep attenuation and stabilization stage. In the creep acceleration stage, the creep speed of the sample increases sharply. The accelerated creep occurs in the annular direction before in the axial direction, and the cyclic acceleration creep rate is higher. In addition, it was found that the steady-state creep speed increased with the increase of stress level, and the annular steady creep speed increased more quickly than the axial creep speed, suggesting that the annular creep speed was much more affected by stress level.The non-linear creep model with fractional derivative established in this paper can simulate the whole creep process well and has high accuracy.