This paper proposes a topology optimization design method for turbulent flow problems considering Non-Newtonian fluid such as blood and polymer solution. Non-Newtonian fluid does not obey the Newtonian relationship between the shear stress and shear rate. Fluid-structure interaction involving Non-Newtonian fluid has a wide range of application in oil and gas, chemical, food industries, microfluidics, and bio-engineering. The TOBS (Topology Optimization of Binary Structures) method is applied to solve the material distribution problem. The TOBS approach uses binary {0,1} design variables, which can be advantageous when dealing with wall function in turbulent flow during optimization. The finite elements method is used to solve the forward fluid Reynolds Averaged Navier Stokes (RANS) equations and output the sensitivities using automatic differentiation. The TOBS optimizer provides a new set of {0,1$\} variables at every iteration with updated geometry through a geometry trimming procedure. Optimization results show that Non-Newtonian effects have a significant influence on turbulent flow design.