The boundary layer problem of a power-law fluid flow with fluid injection on a wedge whose surface is moving with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. The free stream velocity, the injection velocity at the surface, moving velocity of the wedge surface, the wedge angle and the power law index of non-Newtonian fluid are assumed variables. The fourth order Runge-Kutta method modified by Gill is used to solve the non-dimensional boundary layer equations for non-Newtonian flow field. Without fluid injection, for every angle of wedge beta, a limiting value for velocity ratio lambda (cr) (velocity of the wedge surface/velocity of the uniform flow) is found for each power-law index n. The value of lambda (cr) increases with the increasing wedge angle beta. The value of wedge angle also restricts the physical characteristics of the fluid to be used. The effects of the different parameters on velocity profile and on skin friction are studied and the drag reduction is discussed. In case of C = 2.5 and velocity ratio lambda = 0.2 for wedge angle beta = 0.5 with the fluid with power law-index n = 0.5, 48.8% drag reduction is obtained.