The three-stage creep behavior of asphalt mixture could be considered as the results of a competition between damage and hardening. Therefore, the damage and hardening variables were both introduced into Burgers model for modification. The series-wound dashpot in Burgers model was modified with a hardening variable and the undamaged mechanistic model was derived from rheological. Then, Kachanov's equation of damage evolution was adopted and a new creep constitutive model coupled with damage was established by Lemaitre's effective stress principle. Subsequently, static creep tests of two asphalt mixtures were conducted to validate the modified model, and an algorithm was established to determine the model parameters from typical laboratory data. The proposed model and algorithm were demonstrated through laboratory test results, and the analysis results matched the test perfectly. It is indicated that the proposed model can describe the three-stage behavior well.