DEM modeling of granular materials composed of viscoelastic particles can provide valuable insights into the mechanical behavior of a wide range of engineering materials. In this paper, a new model for calculating the normal contact force between visoelastic spheres is presented based on contact mechanics that takes the mechanical behavior of the DEM particles into account. The model relies on an application of the viscoelastic correspondence principle to elastic Hertz contact. A viscoelastic relaxation function for the contact is defined and a generalized Maxwell material is used for describing this function. An analytical expression for the increment in contact force given an increment in overlap is derived leading to a computationally efficient model. The proposed model provides the analytical small deformation solution upon loading but provides an approximate solution at unloading. Comparisons are made with FEM simulations of contact between spheres of different sizes of equal and dissimilar materials. An excellent agreement is found between the model and the FEM simulations for almost all cases except at cyclic loading where the characteristic times of the viscoelastic behavior and the loading are similar.