A numerical analysis is performed to investigate the effect of rotation on the blood flow characteristics with four different angular velocities. The artery has a cylindrical shape with 50% stenosis rate symmetrically distributed at the middle. Blood flow is considered a non-Newtonian fluid. Using the Carreau model, we apply the pulsatile velocity profile at the inlet boundary. The period of the heart beat is one second. In comparison with no-rotation case, the flow recirculation zone (FRZ) contracts and its duration is reduced in axially rotating artery. Also wall shear stress is larger after the FRZ disappears. Although the geometry of artery is axisymmetry, the spiral wave and asymmetric flow occur clearly at the small rotation rate. It is caused that the flow is influenced by the effects of the rotation and the stenosis at same time.