Pulsatile flow of blood through an inclined tube in the presence of an axially nonsymmetrical mild stenosis with a velocity slip at stenotic wall has been investigated in this paper. Blood has been represented by Casson fluid. By employing a perturbation analysis, analytic expressions for the velocity profile, flow rate, wall shear stress, effective viscosity, plug-core velocity and plug-core radius are derived. The influence of stenosis height, shape, slip velocity and inclination of the tube on various flow variables is represented graphically and discussed. Graphical results reflect that wall shear stress and effective viscosity decrease with velocity slip at wall.