Different temperatures and continuous loads have significant effects on the long-term performance of asphalt concrete facings. The effects of temperature and stress on creep strain and creep rate were analyzed by designing a bending creep test of impermeable asphalt concrete under different temperatures and stresses. Based on the test data, a time–temperature–stress-dependent creep constitutive model was constructed to predict the long-term creep behavior of asphalt concrete at low temperature. The results showed that the creep behavior of asphalt concrete showed significant temperature and stress dependence. The creep behavior accelerated as the temperature or stress increased, especially under high-stress conditions, indicating obvious nonlinear characteristics. Under the condition of 0.2376 MPa, when the temperature increased from 0 °C to 20 °C, the strain at the creep time of 9330 s nearly increased by 24 times. Under 0 °C, the loading stress increased from 0.2376 MPa to 1.3176 MPa, and the strain nearly increased by six times at a creep time of 880 s. The creep strain is expected to increase to 8% after 8 years at −15 °C and 0.2376 MPa. The results can provide a scientific basis for engineering practice and significant implications for designing and maintaining asphalt concrete facings.