Previous constitutive models of granite shear creep have two limitations:(1) although moisture greatly affects granite shear creep behavior, currently there are no constitutive models that include this factor;(2) there are also no models that include an acceleration stage. This paper presents an improved Burgers constitutive model with the addition of a damage parameter to characterize the moisture effect and uses a nonlinear relation equation between stress and strain for inclusion as the acceleration stage. The damage parameter is determined from granite creep experiment under four different moisture contents(0%, 0.22%, 0.49%, and 0.79%). The nonlinear relation equation is obtained by fitting a dataset of stain versus time under five different loading stages. To verify the presented model, a creep experiment was conducted on other granite samples and the results show that the model agrees well with the experimental observation data. Previous constitutive models of granite shear creep have two limitations: (1) although major movement of granite shear creep behavior, currently there are no constitutive models that include this factor; (2) there are also no models that include an acceleration stage. This paper presents an improved Burgers constitutive model with the addition of a damage parameter to characterize the moisture effect and uses a nonlinear relation equation between stress and strain for inclusion as the acceleration stage. The damage parameter is determined from granite creep experiment under four different moisture contents ( 0%, 0.22%, 0.49%, and 0.79%). To verify the presented model, a creep experiment was conducted on other granite samples and the results show that the model agrees well with the experimental observation data.