Abstract Non-Newtonian fluid flows through packed beds are common in many industries. Our understanding of this flow system is very limited, and the correlations for describing the fluid-particle interaction are not fully established. To overcome these problems, this paper presents a comprehensive study of this system on a sub-particle scale, with a special reference to the interaction between fluid rheology and bed properties. This is done by conducting about five hundred Lattice Boltzmann simulations under different conditions. The fluid rheology is represented by the power-law model to consider the shear-thinning, shear thickening and Newtonian behaviors of fluids. The simulation condition covers a wide range of bed porosity, particle size distribution and Reynolds number (Re). The results show that the effect of fluid rheology on the fluid behavior is strong. This effect varies significantly with bed porosity which is a function of particle size distribution. The interplay between fluid rheology and bed properties is however not strong in determining the distributions of particle-fluid interaction force. Based on the simulation data, a new drag correlation is established and validated against the experimental data in the literature. This correlation is more accurate and consistent than those reported in the past. It can estimate the mean drag forces on individual particles of different sizes, and is recommended to be used generally in the modeling of particle-fluid flows either for Newtonian fluids or for non-Newtonian fluids obeying the power-law model.