The enriched finite element method was developed for three dimensional fracture problems in a linear viscoelastic body. To manifest the singularity at the crack tip, the 8 node hexahedral enriched elements and corresponding transition elements were employed, combined with ordinary elements on the zone far away from the crack tip. Three types of elements were used together to form the whole mesh. Based on the boltzmann superposition principle, the incremental constitutive relation for viscoelastic materials was formulated. Furthermore, the incremental formulations of the enriched FEM were derived. The strain energy release rate in a cracked viscoelastic body was obtained through the enriched degree of freedoms. The numerical results show that the present method is accurate and efficient.