Abstract: The incremental enriched finite element method (FEM) is developed for fracture problems in a linear viscoelastic body. To manifest the singularity at the crack tip, the quadrangular enriched elements and corresponding transition elements are employed, combined with ordinary elements used on the zone far away from the crack tip. The displacement mode of enriched elements is constructed by enriching the crack-tip asymptotic displacement fields, and that of transition elements is constructed by introducing a zeroing function based on the enriched elements. The role of the transition elements which are placed between the enriched elements and ordinary elements is to eliminate displacement field incompatibility. Based on the Boltzmann superposition principle, the incremental constitutive relation for viscoelastic materials is formulated. Further, the incremental formulations of the enriched FEM are derived. The strain energy release rate in a cracked viscoelastic body is obtained through the node displacement near the crack tip. The numerical results show that the present method is accurate and efficient.