Capability to effectively discretize a problem domain makes the finite-element method an attractive simulation technique for modeling complicated boundary value problems such as asphalt concrete pavements with material non-homogeneities. Specialized "graded elements" have been shown to provide an efficient and accurate tool for the simulation of functionally graded materials. Most of the previous research on numerical simulation of functionally graded materials has been limited to elastic material behavior. Thus, the current work focuses on finite-element analysis of functionally graded viscoelastic materials. The analysis is performed using the elastic-viscoelastic correspondence principle, and viscoelastic material gradation is accounted for within the elements by means of the generalized iso-parametric formulation. This paper emphasizes viscoelastic behavior of asphalt concrete pavements and several examples, ranging from verification problems to field scale applications, are presented to demonstrate the features of the present approach.