The present analysis gives an idea about the Hall current effect on an unsteady Magneto Hydro Dynamic flow of an incompressible viscous, electrically steering fluid through a vertically symmetric artery but horizontally non-symmetric arterial with a mild stenosis. Numerical observations of the laminar flow of a power law fluid in a multiple stenosed artery, in the existence of transverse magnetic field. Now, Hall current effect is taken in to consideration. The transformed governing equations in the present study were solved numerically by using FDM. Effect of stenosis, magnetic field , the Hall current parameter „ ‟, and power law fluid index „ ‟ on the velocity profiles, the wall shear stress and the axial flow are presented graphically.