Three-dimensional direct numerical simulations of the motion of a Newtonian drop rising in Carreau-Yasuda model fluids were carried out by a coupled level-set/volume-of-fluid (CLSVOF) method. Our numerical approach simulated faithfully the physical shear-thinning properties and 3D-nonlinear dynamics that are observed in experiments. Three-dimensional computational results showed that the local change in viscosity around a drop greatly depended on the drop shape and the shear-thinning properties of the quiescent liquid. We quantitatively considered the drop rise motion based on the modified dimensionless numbers (Re-M and M-M) and the effective viscosity.