The results of three-dimensional numerical simulations of the dynamic motion of single drops rising in viscoelastic Chilcott-Rallison (FENE-CR) model fluids are presented. The simulations are performed using a combination of a coupled level-set/volume-of-fluid (CLSVOF) method and a hydrodynamic scheme with formal second-order accuracy. In our study, we address the rising motion of a drop exhibiting a range of small to large deformations. It is shown that the dynamic motion of the drop largely depends on the FENE-CR model parameters: the extensibility parameter L and the Deborah number strongly influence the viscoelastic characteristics of the drop. It is numerically shown that these parameters determine the characteristic cusp formation at the tail of the drop, similar to the case of bubble motion. We also discuss the difference between drop motion and bubble motion in viscoelastic FENE-CR model fluids.