Abstract: Taking thermalviscoelasticity theory as a guide, the stress relaxation test of asphalt mixtures is studied in different temperature environment. The test data are analyzed and the interrelated model parameters are fitted by use of the time-temperature equivalence principle of the thermo-rheologically simple materials. Based on the test results, a generalized Maxwell model is established to simulate the viscoelastic property of asphalt mixtures. And the incremental thermalviscoelastic constitutive relation under nonconstant, nonuniform temperature conditions is obtained from theoretical derivation. Furthermore, a numerical method for thermalviscoelastic analysis of asphalt pavement is provided by using the incremental constitutive relation. At last, the rationality for the constitutive relation and its numerical method is examined by simulating Thermal Stress Restrained Specimen Test (TSRST), and an application case is given.