The classic Burgers creep model could only describe the behavior of rock material before the third creep-phase. The fractional element

defined by using fractional derivative

is an element between spring and dashpot. Through the substitution of a dashpot by a fractional element

a fractional Burgers model is developed. Moreover let the dashpot acted in series be a nonstationary parameter of time for describing the acceleration stage of rock creep. Their constitutive relation and creep compliance are obtained. When the nonstationary dashpot work or does not work

the model could respectively describe two-phase and three-phase creep. It is shown that the creep testing curves under different conditions are coincident well with the theoretical curves. The model can well describe the variation of creep in the period of attenuation

steady period and the period of acceleration. The validity of the model is verified by the experiment data