Abstarct: Increasing cardiovascular disease has led many researchers to consider investigating the flow of blood through the arteries. An important hemodynamic parameter in determining the location and progress of the cardiovascular disease is wall shear stress (WSS). However, the shear stress on the wall modifies at different times and is not able alone to express the stenosis. Oscillatory shear index (OSI) as a hemodynamic parameter, represents the increase of residence time and oscillatory wall shear stress. In this study, a three-dimensional analysis of the non-Newtonian blood flow was carried out using numerical methods of fluid-structure interaction in the bifurcation of the left coronary artery. Physiological conditions were considered first normal and then compliant with hypertension disease and different hematocrit with the aim of evaluating hemodynamic parameters and a better understanding of the onset and progression of atherosclerosis plaques in the region of coronary artery bifurcation. Since the wall shear stress in the time unit solely does not exhibit high risk areas, the oscillatory shear index changes in arterial regions were investigated by modeling the left coronary artery bifurcation with a resilient wall and applying normal and abnormal conditions. In this study, the non-Newtonian Kasson model with 45% hematocrit was employed for models with unhealthy physiological conditions. Both LAD and LCx branches were compared with LMCA branch. It was revealed that there is a mean velocity deficit of 25.51% and 19.07% in the LAD branch, and 48.21% and 43.31% in the LCx for hypertension and elastic 2.2MPa models respectively. As a result of bifurcation, noticeable velocity reduction and backflow formation, a significant decrease happened in shear stress and made it oscillatory at the starting point of the LCx branch which caused the shear stress to be less than 1 Pa and 2 Pa in the LCx and the LAD branch respectively. The difference in WSS in the posterior and anterior at the beginning of LAD and LCx is about 44% and 57%, respectively. Comparing the results of this study with previous clinical investigations shows that the areas with low wall shear stress less than 1.10 Pa along with high OSI value more than 0.3 are in more potential risk to the atherosclerosis plaque development. In result of blood concentrations increase, average velocity reduced to 32.74%, hematocrit, shear stress, and wall displacement increased to 65%, 26.83%, and 8.80% respectively compared to 15% hematocrit of the left coronary arteries.