The subject matter of this investigation is that of establishing a better understanding of the rheological and hydrodynamic behaviour of a fully developed turbulent flow of the Non-Newtonian fluids through a cylindrical pipe, in additional to ascertaining the accuracy and reliability of the laboratory code present findings, via analysing and discussing the evolution of the main rheological and flow predicted results. Toward this end, a fully developed turbulent flow of a power-law fluid describing by a shear thinning fluid with a flow index of 0.75 in an isothermal axially stationary cylindrical pipe, with domain length of 20R and an adequate grid resolution of 65 3 gridpoints in the axial, radial and circumferential directions, has been performed numerically by means of a Large eddy simulation (LES) approach with an extended Smagorinsky model, at a simulation's Reynolds number of 4000. The main present findings show a good qualitative agreement with the numerical and experimental data, where these findings suggest that the increased shear rate of the shear thinning fluid results in a pronounced enhancement in the mean axial velocity compared to the Newtonian fluid especially in the logarithmic and the core regions. The apparent viscosity of the shear thinning fluid enhances gradually out of the viscous sublayer towards to the pipe core region where the shear thinning fluid becomes more and more viscous, in turn the friction factor exhibits a slightly attenuation.