The flow of blood in an inclined artery with an axially non-symmetrical but radially symmetrical mild stenosis has been presented in this study. To account for the slip at stenotic wall, hematocrit and inclination of the artery, blood has been represented by a particle-fluid suspension. The expression for the flow characteristics, namely, the impedance (resistance to flow), the wall shear stress and the shear stress at the throat of the stenosis have been derived and represented graphically with respect to different flow parameters. The impedance increases with the hematocrit and stenosis size but decreases with slip at wall and angle of inclination of the artery. The shear stress at the maximum stenosis height increases with the inclination of the artery but possess the characteristics similar to that of impedance with respect to other parameters. As an application, theoretical values of effective viscosity computed with the help of the present analysis are compared with experimental results and found that they are in reasonable agreement for low hematocrit values in small blood carrying vessels.