Abstract: The incremental enriched finite element method (FEM) is developed for viscoelastic interface crack problems. According to the basic displacements fields of elastic interface crack tip, the crack tip displacement fields of viscoelastic interface crack are derived through the correspondence principle and an approximate Laplace inverse transform method. By incorporating the displacement expressions to the common element, the displacement models of enriched and transition elements are obtained, and then the incremental formulations of the enriched FEM are deduced. The fracture parameters, stress intensity factors and strain energy release rate can be obtained through solving the finite element equation. The enriched finite element model of typical plane problems containing viscoelastic interface crack are constructed, and the fracture parameter solutions show that the presented method is quite accurate for both elastic/viscoelastic and viscoelastic/viscoelastic interface crack and can reflect the creep and relaxation characteristics. It can be applied to the fracture analysis of viscoelastic interface crack.