In the study, two different arterial bifurcation model geometries were used in the flow simulation. The model 1 is assumed the internal carotid artery (ICA) and the external carotid artery (ECA) branches of the bifurcation aligned in parallel to each other, while the model 2 is the typical carotid geometry. In the computation the Non-Newtonian behavior of blood was described using Carreau model. Generally, in the comparison between Newtonian and Non-Newtonian results good agreement was observed in the velocity profiles, while some discrepancies were found in the temporal wall shear stress (WSS) distributions as well as pressure profiles due to the shear thinning behavior. The temporal evolution of WSS periodically increases and decreases closely that of the inlet velocity waveform. It was also observed that the reversed flow region in the ICA of model 2 is 2.5 times larger than that of model 1. As a result, the variation of the flow characteristics can be dependent on the geometry as well as the arterial bifurcation geometry plays an important role in the development of atherosclerosis.