Alterations in whole blood viscosity due to hemodialysis, pathologies or a low stress hemo-dynamic blood flow impact the viscosity generating local changes in blood pressure, blood flow rate, vessel cross sectional area, and giving unexpected global variations over the circulatory network. Despite this fact all 1D models use Newtonian viscosity rheological laws inside. We present a 1D generalized time dependent non Newtonian model of viscosity and we compare the numerical predictions to experimental data of blood rheology available into the literature. We explore two well documented shear stress protocols and we show that the proposed 1D generalized non Newtonian model computed over an arterial segment compares accurately, qualitative as well as quantitatively, the time dependence of the shear stress over the rheological blood data. We hope that 1D generalized blood non Newtonian flow model inside of large numerical 1D models will be useful to help even more the understanding of the global blood dynamics in micro and macro-circulatory networks. 1 Introduction One dimensional flow models is an useful option for computing blood circulation in complex networks either for micro or macrocirculation. One of the main reasons is their capability to furnish good predictions in terms of blood pressure and blood flow rate being costless in terms of time computing compared to the complexity and time consuming of 3D approaches. We note that both the 1D and the 3D approaches are both derived from the same mass and momentum conservation principles. Although we know that alterations in blood viscosity impact the whole blood circulation, in the literature until now all proposed 1D hemodynamic models for studying blood flow circulation are New-tonian: the viscosity is then considered constant. The Newtonian hypothesis is very often well supported