Abstract: A high-order finite volume method (FVM) is proposed for simulating three-dimensional flow of pseudoplastic fluids in this paper. The relationship of shear stress and shear rate of pseudoplastic fluids is nonlinear, which will impose a special difficulty to the calculating process. The power-law model is used to quantitatively describe the rheological behavior of pseudoplastic fluids. In order to avoid the singularities of viscosity at zero and infinite shear rates, the non-uniform initial velocity field is adopted and a strategy of limiting the range of apparent viscosity is proposed. The high-order finite volume method for three-dimensional laminar flow of pseudoplastic fluids is verified in both a straight tunnel and a strongly curved duct. The finite-volume solutions are the numerical values of the friction factor-Reynolds number relation in a straight tunnel for different power-law indices. The results agree well with previous experimental and numerical studies.