Burgers model could only describe the first two stages of rock creep, it is difficult to reflect the accelerate creep stage. In order to describe the whole process of creep and expand its range of application, considering time effect of creep parameters and the effects caused by damage, the following methods should be taken to improve the Burgers model: non-stationary viscous element is used to replace stationary viscous element in a series of Burgers model so as to describe the accelerate creep stage. At the same time, according to the change of damage variable characteristics, a function is assumed and can be put into Kelvin model by Lemaitre strain equivalence principle; finally got the model to describe the creep decay stage. Through combining all divisions, a non-stationary model for rock creep considering damage is obtained. Through analysis, the results show that: the accelerate creep stage can be well described by improved Burgers model; the non-stationary Burgers model curve and experimental curve both approximately consist with each other; the correlate coefficient is high and all parameters are in reasonable ranges. Therefore, the non-stationary Burgers model is feasible and correct; in addition, it is more suitable to describe creep curve of rock under different stress states.