We develop parallel domain decomposition based algorithms used for numerical simulation of blood flows in arteries based on a non-Newtonian viscosity model and provides a comparative study with the numerical results obtained by using Newtonian case.The high nonlinearity and complex geometry make the problem more challenging and parallel computing necessary.Numerical investigation on how the wall shear stress,the streamlines,and pressure distribution depend on different physiological conditions and arterial geometries will be reported.