We conduct a numerical study on the formation process of vortex rings that were observed in a previous experimental study. The numerical simulation of the process is challenging since it is a three-dimensional problem involving unstable drop motion. We use a method in which a three-dimensional domain is discretized; the coupled level-set/volume-of-fluid (CLSVOF) method is used to determine the motion of the drop interface and a sharp interface treatment is used for enforcing the boundary conditions at the drop interface. It is numerically shown that there are two different evolution regimes for vortex ring motion, depending on the value of the Eotvos number (Eo). The simulation results show that the transient evolution process of a vortex ring is sensitive to the drop size. Thus, our results agree with those of the previous experimental study. We also explore the effect of the viscosity ratio (=mu(D)/mu(C)) on vortex ring formation resulting from a falling drop.