Based on the trabecular beam bending and creep test and direct tensile stress relaxation test, the creep rate, relaxation time, relaxation modulus and other rheological indicators were used to compare and analyze the polyphosphoric acid(PPA) SBS composite modified asphalt mixture and SBS modified asphalt mixture under different low temperature conditions. Through the low temperature rheological properties of modified asphalt mixture, combined with damage mechanics and viscoelastic mechanics, a creep damage model and a six element generalized Maxwell stress relaxation model were proposed. The results show that the PPA SBS composite modified asphalt mixture enters the creep stability period earlier than the SBS modified asphalt mixture under different low temperature conditions, and its cumulative deformation and creep rate are greater than that of the SBS modified asphalt mixture; based on the Burgers model, the creep damage model established in combination with damage mechanics can better reflect the deformation characteristics of the three stages of creep damage. The stress relaxation ability of the two asphalt mixtures is almost the same at 10℃, while the stress relaxation ability of PPA SBS composite modified asphalt mixture at 0℃, -10℃ and -20℃ is better than that of SBS modified asphalt mixture, and the lower the temperature, the more obvious the effect; the six element generalized Maxwell model can be used to better describe the stress relaxation characteristics of asphalt mixture under low temperature conditions.