A numerical analysis has been performed for developing turbulent flow of non-Newtonian fluid in eccentric annular passage. Several calculations have been carried out to examine the drag reduction with decreasing power index of power-law fluids and the reduction of skin friction factor with increasing eccentricity defined by the distance between the centers of the inner and outer pipes for Newtonian fluid. In numerical analysis, the power law model for non-Newtonian fluid and an algebraic Reynolds stress model for turbulent flow were adopted in order to predict precisely non-Newtonian flow behaviour. Boundary-fitted coordinate system was introduced as the method of coordinate transformation. The numerical results are compared with the experimental data involving stramwise velocity and fluctuating velocities in axial, radial and tangential directions. As a result of comparison with the experiment, it was found that the present method could predict well the streamwise meam-velocity in both fluids and reproduce the secondary flow of the second kind generated by anisotoropic turbulence. As for the comparison of fluctuating velocities, the agreement with experimental data is more satisfied for Newtonian fluid than for non-Newtonian fluid. The calculated results also suggest that the drag reduction with polymer solution is realized by the present method as well as the experiment and the phenomenon of decaying fluctuating velocity with decreasing power index is predicted.