In the present study, we numerically investigated drag-reducing turbulent channel flows by surfactant additives. Surfactant additives were assumed to be uniformly distributed in the entire flow region by turbulent convection and diffusion, etc., but it was assumed that the shear-induced structure (SIS) (network of rod-like micelles) could form either in the region next to the walls or in the center region of the channel, making the fluid viscoelastic. In other regions surfactant additives were assumed to be incapable of building a network structure, and to exist in the form of molecules or micelles that do not affect the Newtonian properties of the fluid. With these assumptions, we studied the drag-reducing phenomenon with coexisting Newtonian and non-Newtonian fluids. From the study we identified the effectiveness of the network structures at different flow regions, and showed that the phenomenon of drag-reduction (DR) by surfactant additives is not only closely associated with the reduction of Reynolds shear stress but also related to the induced viscoelastic shear stress.