Non-Newtonian fluids have not been frequently considered in different research although they are common fluid type in the industry and environment in comparison to Newtonian fluids. In this paper, a non-Newtonian fluid with a shear-thinning property is considered in a specific geometric condition. The flow is considered to be laminar, and the geometric subject of the research is a rectangular duct with an obstacle, which is assumed to be in the middle of the duct with a height of half the duct width. This research provides a numerical solution using a written MATLAB code with a SIMPLEC algorithm and a power law model. This code is validated by comparing code results with analytical results for a specific condition. The results of this research show variations of velocity and viscosity in the duct, which can be extremely useful in future research and applications, not only because of frequent usage of shear-thinning fluids in industrial applications but also because of the common duct shape facilities in different processes in several industries.