We present the results of three-dimensional direct numerical simulations of the dynamic motion of a gas bubble rising in Carreau model fluids. The simulations are carried out by a coupled level-set/volume-of-fluid (CLSVOF) method, which combines some of the advantages of the volume-of-fluid (VOF) method with the level-set (LS) method. In our study, it is shown that the motion of a rising gas bubble largely depends on the Carreau model parameters, n and B (n, the slope of decreasing viscosity and B, time constant). Both the model parameters, n and B, have considerable influence on the bubble rise motion. Using numerical analysis, we can understand in detail the bubble morphology for non-Newtonian two-phase flow systems. We also discuss bubble rise motion in shear-thinning fluids in terms of the effective viscosity, η_eff, the effective Reynolds number, Re_eff and the effective Morton number, M_eff.